The defendant appeals his first degree murder convictions and consecutive sentences of death, which were imposed consecutively to sentences for two convictions of robbery, two convictions of kidnapping and one conviction for theft of property valued in excess of $1000. We have jurisdiction under A.R.S. § 13 — 4031 and Ariz. Const, art. 6 § 5(3).
The defendant raises fifteen issues in this appeal, which may be grouped into three categories. The first is pre-trial issues:
1. Was the defendant denied effective assistance of counsel during the pretrial period?
2. Did the trial court err in denying the defendant’s motion to recuse the prosecutor?
3. Did the trial court err in its method of determining if the defendant was competent to waive his right to counsel?
4. Did the defendant make a proper • waiver of his right to counsel?
5. Did the trial court err in denying the defense motion to suppress evidence based on a policeman’s investigation of the license plate of the automobile the defendant drove when arrested?
6. Did the trial court err in denying the defense motion to suppress certain post-arrest statements made by the defendant?
The second category of issues raised by the defendant relates to decisions of the court during trial, including:
7. Was it error to keep the defendant in leg shackles during the trial?
8. Was it error to admit the testimony of a former robbery victim of the defendant?
9. Was it error to admit into evidence the items found in the car that defendant was driving at the time of his arrest?
10. Was it error to admit some 71 large color photographs of the victims into evidence?
11. Was it error to order the defendant’s advisory counsel to submit jury instructions over the objection of the defendant?
The final category of issues concerns the validity of our method of determining the propriety of the death penalty, including:
12. Does the death penalty statute violate the eighth amendment’s prohibition against cruel and unusual punishment?
13. Is it improper for any entity other than a jury to determine aggravating and mitigating circumstances?
14. Is it unconstitutional to require the defendant in a capital case to prove mitigation?
15. Is our death penalty statute void-for-vagueness for lack of definition of the standard “especially cruel, heinous and depraved”?
The facts necessary for a determination of the issues presented here are these. Robert A. Wise, district supervisor for KAR Car Products Incorporated, left Mesa, Arizona on 24 January 1980 to meet with Martin L. Coneannon, the corporation’s area sales representative in Tucson. Wise checked into a Tucson motel that evening, *283and on the following day accompanied Con-cannon on sales calls in southern Arizona. The two men returned to Wise’s motel in the late afternoon of 25 January 1980.
Their bodies were discovered in Wise’s motel room the following morning. Robert Wise was found on the floor next to the bed, tethered to a bedpost by a restraint wrapped around his neck. He had been bound with his hands behind his back, with his ankles tied together and secured to the hand ligatures. Wise had been shot once in the chest from a few inches distance with a .25 caliber pistol. This wound perforated his spinal cord and was the cause of death. In addition, he had been shot in the left temple from a distance of no more than three inches. He had been further bludgeoned with a motel lamp, causing abrasions of the head and skull, broken teeth and multiple fractures of the right side of the jaw. Chips broken from the wooden lamp were removed from this victim’s right temple and mouth.
Mark Concannon’s body was found in the bathroom area of the room, head resting on a pillow. Like Wise, he had been shot in the left chest region at close range, and the chest wound similarly perforated his spinal cord. Like Wise, Concannon had been shot near the temple from no more than three inches distance. Unlike Wise, however, Concannon did not die instantaneously from these wounds. According to the medical examiner, this victim lived a short time after being shot. The examiner testified to three other findings concerning Concannon. He found hemorrhages at the base of Con-cannon’s neck caused by bindings secured there. Second, he found evidence of “defensive wounds” in the form of black and blue marks over Coneannon’s knuckles of the sort sustained while trying to ward off blows. Finally, he had removed a pair of calf length men’s dress stockings from the mouth of this victim, socks which had been pushed to the back of his throat, thereby obstructing his breathing passage.
The two victims had been bound and otherwise restrained with dozens of strips of bedding material, shoelaces and their own clothing before their executions. Their bodies were covered with blankets. Robert Wise’s briefcase, containing his credit cards, was removed from the motel. Mark Con-cannon’s borrowed Oldsmobile was taken from the motel parking lot.
At 8:40 p.m. on 25 January 1980, the defendant appeared at the Mesa home of Robert Wise. The defendant carried in one hand Wise’s business card, and after falsely identifying himself, inquired whether “Bob” Wise was at home. After a brief conversation with the victim’s wife, the defendant departed.
At about 5:30 p.m. on 26 January 1980, the defendant drove Concannon’s borrowed Oldsmobile into a reserved parking, lot on the campus of Northern Arizona University in Flagstaff, Arizona. The campus policeman monitoring use of the lot advised the defendant that it was a restricted lot and directed him to another location. During their conversation, the officer observed that the defendant was wearing two jackets, and that while he was driving a car bearing Ohio license plates, the defendant seemingly spoke with a southern accent. These circumstances aroused the officer’s suspicion, and noting the license number of the vehicle, the officer called his police dispatcher and asked him to check the license number. As the defendant drove away from the encounter, the dispatcher reported that the car was stolen and was possibly involved in two homicides in Tucson.. With the aid of two other officers, the Oldsmobile was stopped, and the defendant arrested and searched. The officer removed a .25 caliber automatic pistol from the pocket of one jacket worn by the defendant, and seized a black identification case containing one badge inscribed “Security Guard,” another inscribed “Special Officer,” a Texas driver’s license and a partial (cut in half) Oklahoma driver’s license, both issued to Ronald Gene Svetgoff. The first officer asked the defendant if he was Svetgoff, and he replied that he was, and explained the lack of resemblance to the license picture owing to changes in hairstyle and weight. The automobile was towed to stor*284age and the defendant held. Tucson authorities flew to Flagstaff where they inventoried the contents of the Oldsmobile and arranged for the defendant’s return to Pima County.
The defendant was held in custody until his trial, which began 21 April 1982. During October of 1980, the defendant committed an assault on a fellow jail inmate, and was convicted on 30 July 1981 of Dangerous or Deadly Assault by Prisoner, a felony for which he was sentenced to life imprisonment without possibility of parole for twenty five years. See A.R.S. § 13-1206. As to the charges in the instant case, the defendant insisted on serving as his own counsel, and the trial court ordered a public defender to act as advisory counsel. Prior to the trial the defendant threatened specifically to harm his advisory counsel, and generally threatened the participants in the trial. As a result of these threats, the court ordered that the defendant be shackled with leg irons for the duration of the trial. The defendant at trial conducted no direct examination, asked only one question on cross examination, and made no jury arguments.
At the close of the evidence, over strenuous objection by the defendant, the court ordered advisory counsel to submit proposed jury instructions. The defendant discarded the copy of these instructions provided him by advisory counsel. The trial court considered the advisory counsel-submitted instructions, and on its own motion, with the defendant’s assent, added an instruction on the defendant’s right not to testify. The defendant was also given an additional day to submit instructions of his own design, but he failed to do so and his request for a further continuance for this purpose was denied. His convictions for first degree murder, A.R.S. § 13-1105, robbery, A.R.S. § 13-1904, kidnapping, A.R.S. § 13-1304, and theft, A.R.S. § 13-1802, followed.
At the defendant’s sentencing hearing, the trial court invited him to present factors in mitigation, and offered to allow the defendant additional time to do so. The defendant declined, and the trial court thereafter found as aggravating circumstances that the defendant had a prior felony conviction for the deadly assault for which life imprisonment was imposable; that that same crime involved the use of violence; that the defendant committed the instant crimes for pecuniary gain; and that the instant murders were committed in an especially cruel, heinous or depraved manner. The trial court found no mitigating factors sufficient to overcome the aggravating factors and sentenced the defendant to death penalties for the murders of Wise and Coneannon to be served consecutively one to the other, both to be served consecutively to the sentences imposed for the robberies and kidnappings and the theft of Concan-non’s borrowed vehicle.
PRETRIAL ISSUES
1.
The defendant first contends that he was denied effective assistance of counsel during the pretrial phase. First, defendant alleges that the quality of cross examination and arguments to the court made by the public defenders at the pretrial hearings fell below the standard of minimum competence which we adopted in State v. Watson, 134 Ariz. 1, 653 P.2d 351 (1982). Defendant alleges that the public defenders “did not vigorously respond to the state’s arguments,” and did not respond to several questions posed by the trial court.
We have reviewed the pretrial record in an effort to ascertain whether the performance of the public defenders prior to the defendant’s undertaking of his own defense fell below the Watson standard. We believe that their performance was sufficiently competent to reject the defendant’s general contention of ineffective representation. We find no error.
The defendant further contends, however, that the public defenders failed to file timely a notice of change of judge under Rule 10.2, Arizona Rules of Criminal Procedure, 17 A.R.S. The parties were noticed that this matter was permanently assigned to the trial judge on 8 February 1980. No motion for change of judge was *285filed within the 10 day limit for filing a notice of change of judge under Rule 10.2. Later, on 11 March 1980, the public defenders filed a “Notice of Intention to File Motion Challenging Permanent Assignment of Superior Court Trial Judge.” The basis of the motion was that the defendant was denied his sixth amendment right to an impartial judge because the trial judge assigned to the case had previously sentenced another defendant to death. The evidence indicates that while the judge had imposed the death penalty in one previous case, he had failed to sentence defendants to death in three other capital cases over which he presided. There was no other evidence that he was predisposed to giving the death penalty.
Admittedly, by failing to file a timely motion for change of judge, the defendant lost, the right to preemptorily remove the judge pursuant to Rule 10.2, supra, and had to rely upon removal for cause pursuant to Rule 10.1. We do not believe, however, that this indicates counsel’s performance fell below the minimum professional competence standard set down in Watson, supra, applicable to cases on appeal as of the date of the Watson decision, State v. Nunez, 135 Ariz. 257, 660 P.2d 858 (1983). There is no showing that a change of judge was critical in the first place, because the facts do not support a conclusion that the judge was biased. It was not prejudicial for the public defenders to miss the deadline for changing the judge under Rule 10.2, supra. Under the circumstances, defendant was not denied effective assistance of counsel.
2.
The defendant’s second contention is that his constitutional rights to compulsory attendance of witnesses and cross examination were violated when the trial court denied his motions to recuse the prosecutor, and to call him as a witness, because the prosecutor had been present at the time some of defendant’s statements were taken. We do not agree.
Recently, in State v. Jessen, 134 Ariz. 458, 657 P.2d 871 (1982), the defendant sought to call the prosecutor as a witness to testify to the events surrounding the making of his inculpatory statements during his interrogation. The prosecutor avowed to the court that he was never alone with the defendant during the interrogation, and that two other witnesses, police officers present at the interrogations, were able to give accounts of the proceedings. We stated in Jessen, supra, that “[t]he testimony of the prosecutor would have been cumulative of the testimony of the officers. Defendant has shown no issues concerning the interrogation on which the prosecutor would have been the only person to offer evidence.” Id. 134 Ariz. at 462, 657 P.2d at 875. We found no abuse of discretion in the trial court’s denial of the defendant’s motion to call the prosecutor as a witness. Id.
Our disposition of this issue in the instant case is the same. In the arguments on the motion to recuse the prosecutor, the prosecutor avowed that at no time in his contacts with the defendant was he unaccompanied by other police authorities, and the prosecutor’s avowals to the court were corroborated by one of the detectives present at the encounters between the defendant and the prosecutor. We feel, as we stated in Jessen, supra, that the defendant did not show a need for calling the prosecutor as a witness at trial, and the prosecutor’s recusal from the case was not required. In finding no error, however, we wish to reiterate what we have recently stated:
We note the increasing number of cases before this court where the prosecutor is also a witness on some point in issue, usually the admissibility of a confession or statement made by the defendant. This we believe skirts the line not only of the Code of Professional Responsibility, DR5-102, Rule 29(a), Rules of the Supreme Court, 17A A.R.S., but can be a violation of due process. See Annotation, 54 A.L.R.3d 100. Where there is prejudice, we would be compelled to reverse on this point. Prosecuting attorneys in the future should avoid putting themselves in this position. State v. Williams, 136 Ariz. 52, 57, 664 P.2d 202, 207 (1983). See also *286State v. Tuzon, 118 Ariz. 205, 575 P.2d 1231 (1978).
3.
The defendant’s third assertion of pretrial error is that the trial judge did not conduct a proper hearing to determine his competency to waive counsel. We note that beginning in 1980, there were several motions for mental examination under Rule 11.2, Arizona Rules of Criminal Procedure, 17 A.R.S., and some were conducted though the defendant failed to cooperate at times.
On 5 January 1981 the defendant signed a stipulation that his competency be determined on the basis of psychiatric reports filed with the court. On 7 January 1981, after reading the reports of both psychiatrists, the court entered a minute entry finding “that Defendant is able to understand the proceedings against him and assist counsel in his own defense.” Because a defendant is competent to stand trial does not mean the defendant is competent to waive the assistance of counsel. State v. Hartford, 130 Ariz. 422, 424, 636 P.2d 1204, 1206 (1981); see Westbrook v. Arizona, 384 U.S. 150, 86 S.Ct. 1320, 16 L.Ed.2d 429 (1966). Therefore on 23 March 1982 the trial court conducted a hearing to determine whether the defendant should be allowed to represent himself on the murder charge. The court reviewed the facts dealing with the defendant’s education and experiences in the justice system, including a previous waiver of counsel hearing on the prisoner assault charge, and incorporated those facts by reference before ruling that “the defendant [was] able to represent himself.”
We believe the court did not abuse its discretion in determining that the defendant was mentally competent to waive counsel. The trial court in making its determination not only relied here on the psychiatrists’ opinions, but it also observed the defendant’s demeanor and heard his responses to inquiries about procedural matters posed by the court. The record reflects that the defendant was articulate, clearly and forcefully expressing his desire to represent himself. The defendant contends, however, that the trial court gave insufficient weight to the fact that he had years before been diagnosed to have organic brain syndrome. We have said that a mere diagnosis of a mental disease or disorder does not mean that the defendant is unable to make rational decisions regarding his case. See State v. Evans, 125 Ariz. 401, 403, 610 P.2d 35, 37 (1980); State v. Thompson, 113 Ariz. 1, 3, 545 P.2d 925, 927 (1976). We find no error.
4.
Defendant next claims that even if he was competent to waive counsel, the trial court failed to ascertain whether the defendant did, in fact, make a knowing and intelligent waiver of his right to counsel. The defendant’s brief alleges that the trial court
made no effort to warn the defendant of the potential pitfalls that face a lay person in representing himself. The Court did not question the defendant about educational background. The Court did not question how well versed the defendant was in legal procedures and the issues of the case. The Court did not advise him that professional assistance would be beneficial and advantageous to the defendant. The Court clearly failed to apprise the defendant of the dangers inherent in self-representation.
We do not agree.
At the 15 April hearing, as well as the hearings of 15 and 23 March 1982, the defendant’s educational level and his familiarity with the rules of procedure in criminal matters were established. At the later of the March hearings the trial court advised the defendant that his first degree murder charge “could result in the death sentence.” He further told the defendant that “it is a terribly complex, terribly serious case.” He then inquired of the defendant whether in such circumstances he was certain he wanted to represent himself, to which the defendant affirmatively replied. At the April hearing, the trial court advised *287the defendant that the point of having advisory counsel at his table during the trial is that “he would be ready to go in case you decided that you are in too deep of water to continue.”
In Edwards v. Arizona, 451 U.S. 477, 101 S.Ct. 1880, 68 L.Ed.2d 378 (1981), the United States Supreme Court stated that “waivers of counsel must not only be voluntary, but constitute a knowing and intelligent relinquishment or abandonment of a known right or privilege, a matter which depends in each case ‘upon the particular facts and circumstances surrounding that case, including the background, experience and conduct of the accused’.” Id., 101 S.Ct. at 1883-84, quoting Johnson v. Zerbst, 304 U.S. 458, 464, 58 S.Ct. 1019, 1023, 82 L.Ed. 1461, 1466 (1938). And we have stated:
The fundamental question then is not one of the wisdom of the defendant’s judgment but whether the defendant’s waiver of counsel was made in an intelligent, understanding and competent manner. * * * All factors relating to the determination of whether the defendant knew exactly what he was doing when he waived his right to counsel are relevant. State v. Martin, 102 Ariz. 142, 146, 426 P.2d 639, 643 (1967).
We believe that the record complies with the federal and state standards requiring a knowing and intelligent waiver of the right to counsel and assertion of his right to self-representation.
Defendant, however, contends that the failure to sign a written waiver negates the waiver of counsel. Our state constitution in section 24 of article 2, allows a defendant to waive counsel, and Rule 6.1(c) of our Rules of Criminal Procedure, 17 A.R.S., requires that “[a] defendant may waive his rights to counsel * * * in writing, after the court has ascertained that he knowingly, intelligently and voluntarily desires to forego them.” At the end of the 15 April argument on representation, the trial court allowed the defendant to represent himself notwithstanding his refusal to sign a waiver, but ordered Mr. Cooper to serve as advisory counsel.
We have stated that the absence of a written waiver does not constitute reversible error. State v. Evans, supra, 125 Ariz. at 403, 610 P.2d at 37. Under the facts and circumstances of this case as indicated by the hearings, it is clear that the defendant was advised of the charges and possible death penalty and that he was reminded of the complexity of the proceedings and the advantage of advisory counsel. Despite these warnings, defendant waived counsel. We find that the defendant did voluntarily waive counsel, and that such waiver was knowingly and intelligently made. We find no error.
5.
The defendant’s two final pretrial issues both deal with motions to suppress that were denied by the trial court. He first argues that the trial court erred in denying his pretrial motion to suppress physical evidence discovered upon his arrest on the Northern Arizona University campus. The ground for this contention is that the policeman had no right to run a computer records check on the license plate of the automobile the defendant was driving on the campus, and that the resulting arrest violated his fourth amendment right to be free of unreasonable searches and seizures.
The defendant cites no authority for the proposition that a policeman may not conduct a check on a license plate at will even without reasonable suspicion, and we have found none. We believe that there is no expectation of privacy in the license plate affixed to the exterior of one’s motor vehicle driven in public meriting constitutional protection. Also, there was no search or seizure of the vehicle at the time the license check was made. Neither was there a detention of the defendant. By the time the defendant was stopped by the police for the purpose of effecting his arrest, the officers knew that the vehicle had been reported to be stolen and possibly involved in a double homicide. At this juncture, the police had probable cause to arrest the driver. We find no error.
*2886.
The second of the alleged trial court errors on pretrial suppression motion rulings concerns two statements made by the defendant to a Tucson detective which the detective later related at trial. The first occurred at the Flagstaff airport when the authorities were transporting the defendant to Pima County. In response to an officer’s attempt to shield the defendant from the January airport winds by sharing his jacket, the defendant replied “You don’t need to do that, I deserve whatever I get.” The second statement occurred during a conversation at the jail between the defendant and the detective concerning the clothing seized from the defendant upon his arrest. The detective advised the defendant that the clothes were being held in evidence, and the defendant said that something usable might be found on the burgundy shirt and shoes that he had been wearing, but that the other clothing had not been worn. The defendant now claims that these statements were taken in violation of his Miranda rights, and that their admission in evidence violated his fifth amendment privilege against self-incrimination. The basis of this claim is that when the Tucson authorities approached the defendant being held in Flagstaff and read him his Miranda warnings, he invoked his right to silence, so that anything said by him thereafter was inadmissible under Miranda. We do not agree.
The warnings were read at 9:30 a.m. on 27 January in Flagstaff, at which time the defendant stated that he had nothing to say. He was then arraigned. The Tucson authorities departed with the defendant about 2:00 p.m. that day. The statement the defendant made at the airport about his “deserving” his fate was not in response to any questions or prompting by the authorities. It was merely a response to the shielding gesture by the detective. As to the conversation at the Pima County Jail, it began when the defendant asked if he could have some of his clothing returned to him. When the detective replied that it had to be retained as evidence, the defendant indicated that only the shirt and shoes would have probative value. Again, this statement was not in response to any interrogation of the defendant by the detective, or attempt by the police not to scrupulously honor the defendant’s right to remain silent. Rhode Island v. Innis, 446 U.S. 291, 100 S.Ct. 1682, 64 L.Ed.2d 297 (1980); See Michigan v. Mosley, 423 U.S. 96, 96 S.Ct. 321, 46 L.Ed.2d 313 (1975). It was made as a result of a conversation initiated by the defendant, and is admissible in evidence at trial against him. State v. Landrum, 112 Ariz. 555, 559, 544 P.2d 664, 668 (1976) . We find no error in the denial of the two motions to suppress.
TRIAL ISSUES
7.
The defendant’s first assignment of error relating to the conduct of his trial is that his constitutional rights to self-representation and a fair trial were violated by the court’s order that he be shackled during the trial. The defendant complains that his right to self-representation was impaired by not being able to move about the courtroom like the prosecutor at trial. He further asserts that the trial court abused its discretion in ordering the ankle shackling because there was no justification for the restraint.
Although we have stated that “[w]e do not view with favor the shackling of a defendant except for the most compelling of reasons,” State v. Watson, 114 Ariz. 1, 12, 559 P.2d 121, 132 (1976), cert. denied 430 U.S. 986, 97 S.Ct. 1687, 52 L.Ed.2d 382 (1977) , it is still within the sound discretion of the trial court whether to have a prisoner shackled at trial. State v. Starks, 122 Ariz. 531, 534, 596 P.2d 366, 369 (1979); State v. Watson, supra, 114 Ariz. at 11, 559 P.2d at 131. In the instant case, the defendant threatened bodily harm to his appointed advisory counsel and to any other attorney who might subsequently act in that capacity. The court was aware of that threat and the fact that the defendant was disposed to violence, because he was apprised of recent episodes of assaultive behavior by the defendant while in custody. The court noted *289the factors upon which he based his decision on the record in compliance with the rule of State v. Reid, 114 Ariz. 16, 22, 559 P.2d 136, 142 (1976), cert. denied 431 U.S. 921, 97 S.Ct. 2191, 53 L.Ed.2d 234 (1977). We cannot say, on reviewing the record, that the trial court abused its discretion in exercising its responsibility in overseeing the security of the courtroom and of the officers of the court.
Nor do we believe that a defendant, because he is representing himself, has some constitutional right, attendant upon his right to self-representation, to walk about the courtroom during the trial. Since the defendant here was fully able to address the judge and jury and to conduct witness examinations from the defense table, we find no substantive encroachment upon his right to self-representation, even though his immobility might have been inconvenient. We find no error.
8.
The second trial error alleged by the defendant is that the court improperly admitted testimony of Ronald Svetgoff, a robbery victim of the defendant prior to the instant crimes, and Jeri Wise, the widow of one of the victims. The defendant contends that introduction of their testimony, dealing with contacts each had with the defendant, improperly brought before the jury evidence of other bad acts. Such evidence, argues the defendant, was inadmissible under Rule 404(b) of our Rules of Evidence, 17A A.R.S., which states:
(b) Other crimes, wrongs or acts. Evidence of other crimes, wrongs, or acts is not admissible to prove the character of a person in order to show that he acted in conformity therewith. It may, however, be admissible for other purposes, such as proof of motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident.
The state contends that Svetgoff’s testimony was properly introduced to establish identity, intent, and common scheme or plan. We agree.
We have discussed the “modus operandi exception” to Rule 404(b) in these terms:
The modus operandi exception to the rule that evidence of other bad acts is inadmissible has two aspects. A separate act with a similar modus operandi may indicate that the defendant, in the act for which he is on trial, was carrying out a common plan or scheme, (citations omitted) An unrelated bad act with a similar modus operandi may also be admissible to identify the defendant as the one who committed the crime for which he is being tried, (citation omitted)
When utilizing the common scheme exception, the basic test for admissibility is that “[similarities between the offenses * * * must be in those important aspects where normally there could be expected to be found differences.” (citation omitted) Logically, this test should also apply to the admission of evidence under the identity exception. Moreover, in determining admissibility, a court must also consider differences between the acts as well as similarities. State v. Jackson, 124 Ariz. 202, 204, 603 P.2d 94, 96 (1979).
The Svetgoff testimony tends to establish the identity of the murderer of Wise and Coneannon through the similarity of the acts in each incident involving armed robbery of motel guests, both as to the manner of securing the victims and as to the items taken by the perpetrator. Svetgoff testified that he was made to lie down on the floor while his hands were secured with a tie behind his back. His legs were then tied together with a dress shirt. Next his legs and hands were tied together with a jump rope. A sock was stuffed into his mouth and then an undershirt was banded across his mouth and held in place by a belt. This method of hog-tying and gagging the victim with his own clothing was repeated in the binding of the instant victims and the gagging of Coneannon with socks.
Svetgoff also testified that he was dragged into the bathroom area of the motel room, and that the defendant placed a pillow under his head while Svetgoff was lying on the floor. Coneannon was found, *290bound and gagged, on the floor of the bath area of the motel room, head lying on a pillow placed there by his murderer. Finally, Svetgoff testified that his clothes, briefcase and automobile were stolen by the defendant. Robert Wise’s clothes and briefcase were stolen by his murderer, and Mark Concannon’s automobile was stolen in the same incident.
Admittedly, there are differences between the Svetgoff and Wise-Concannon episodes, the most obvious of which is the disposition of the respective victims. But in the “important aspects where normally there could be expected to be found differences” between the offenses, Jackson, supra, the similarities of choice of victims (salesmen motel guests), peculiar method of eliminating resistance (hog-tying with clothing and gagging using socks), placement of victims (in bathroom with heads on pillows), items stolen (briefcases and clothing) and manner of departing the crime scene (via the victim’s automobile) are so striking that we conclude that Svetgoff’s testimony tends to prove the identity of the killer of the instant victims.
Furthermore, the Svetgoff testimony is probative under the common scheme exception to Rule 404(b). There was trial testimony of no evidence of forcible entry into the motel room where the instant victims were found. Svetgoff testified that he was tricked into letting the defendant into his motel room by the defendant’s presentation of false “security guard” badges. The N.A.U. policemen who apprehended the defendant found false security guard badges, along with a driver’s license belonging to Svetgoff. Svetgoff’s testimony, when coupled with that of the arresting officer and of the La Quinta investigating detective, strongly suggests identity and common scheme or plan. Svetgoff’s testimony was relevant and probative.
The testimony of Mrs. Wise about the visit to her home on the evening of the murders by a man she positively identified as the defendant before testifying tends to prove the identity of the murderer. The defendant appeared at her door holding one of her husband’s business cards and asking for “Bob” Wise, according to her testimony. Since the defendant was discovered in possession of Wise’s briefcase and other personalty at the time of his apprehension in Concannon’s car by Flagstaff police, a jury could legitimately infer that he obtained the business card and Wise’s home address as a result of the murder and robbery. Mrs. Wise’s testimony was also relevant and probative.
The relevance and probative value of each witness’ testimony being established, we must evaluate the prejudicial effect of the testimony on the jury. Rule 403 of our Rules of Evidence states:
Rule 403. Exclusion of Relevant Evidence on Grounds of Prejudice, Confusion, or Waste of Time
Although relevant, evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence.
We readily concede that the Svetgoff testimony concerning his victimization by the defendant tends to create an impression of the defendant as a bad man. Nonetheless, we do not believe that the prejudicial effect substantially outweighs the probative value on the identity issue addressed by Svet-goff’s testimony.
With regard to Mrs. Wise’s testimony, assessing its prejudicial effect is problematical. The defendant was in contact with the victim’s wife for but a few moments, made only harmless inquiries, and departed without incident. We can only speculate as to the defendant’s motivation for the visit. However, what appeared to be a seemingly innocuous visit was of great probative value on the issue of identity when considered along with the rest of the evidence. We find no error.
9.
The defendant’s next assertion of trial error concerns the admission of evidence gathered as a result of the search *291under warrant of the stolen car that defendant was driving when he was apprehended. He contends that the warrant was invalid for lack of jurisdiction, and that the subsequent search violated his fourth amendment protection against unreasonable searches. This contention overlooks the basic premise that one must have a legitimate expectation of privacy in the thing searched in order to have standing to object to the validity of the search. A thief of property has no legitimate expectation of privacy in stolen goods. And “this court has refused to recognize as ‘reasonable’ any expectation of privacy a thief may have in an automobile which he has stolen.” State v. Schad, 129 Ariz. 557, 563, 633 P.2d 366, 372 (1981), cert. denied 455 U.S. 983, 102 S.Ct. 1492, 71 L.Ed.2d 693 (1982), citing State v. Myers, 117 Ariz. 79, 570 P.2d 1252 (1977), cert. denied 435 U.S. 928, 98 S.Ct. 1498, 55 L.Ed.2d 524 (1978). We find no error.
10.
On 20 April 1983 the court held a pre-trial hearing which occurred five days after the trial court granted the defendant’s request to represent himself. The defendant, after first objecting to the admission of the photographs in evidence, stated, “I would like to move to admit them all so we can proceed. * * * I withdraw my objection.”
On appeal the defendant claims that certain photographs of the victims had no probative value, were highly prejudicial, and were therefore erroneously admitted into evidence under Rule 403, supra. Ninety-three large, 8 X 10" color photographs were introduced in evidence at the trial. We have no hesitancy in stating that had the defendant maintained a valid objection, we would consider reversing the conviction, because the prejudice of several gruesome photographs among the over 90 admitted outweighed their probative value. We believe that counsel, by “overtrying” his case, could well have placed the conviction in jeopardy. The defendant, however, withdrew his objection to their admission.
Generally, without objection to the admission of gruesome photographs at trial, the issue may not be raised on appeal. See People v. Hines, 61 Cal.2d 164, 37 Cal.Rptr. 622, 390 P.2d 398 (1964); State v. Phipps, 224 Kan. 158, 578 P.2d 709 (1978); State v. Powers, 645 P.2d 1357 (Mont.1982). Because the waiver of objection at trial made by the defendant is valid, he may not raise the issue on appeal.
11.
When it came time to settle instructions, the court advised the defendant that the arguing of instructions was “a highly technical matter.” Although defendant indicated a desire to handle the matter personally, stating, “I won’t accept any instructions from [advisory counsel] because I am representing myself,” the court ordered advisory counsel to provide the defendant with instructions, adding “What you do with them is your business.” The trial court also ordered that advisory counsel participate in the settling of instructions, “because I do believe that is a matter that perhaps * * * you [the defendant] don’t have the competence to handle.”
On 26 April 1982, the defendant tore up the copy of instructions provided by advisory counsel and discarded them in a wastepaper basket. The defendant also informed advisory counsel that he did not want him arguing on his behalf during the settling of instructions, and during the settling of the instructions, the defendant objected to every instruction that was proposed by the state and the defense and to several that the court stated its intention to give. In addition, the defendant advised the court that he did not submit any of his own instructions because the court ordered his advisory counsel to do so, and that he would have prepared them absent the court’s order. After instructions were approved by the court, the defendant was given until the following morning to prepare his own instructions, which the defendant did not do because of a claimed lack of access to the rules of procedure governing instructions. Defendant requested additional time to prepare instructions while renewing his objec*292tion to the submission of advisory counsel’s instructions in his behalf. The court denied the request for additional time, and asked the defendant if he would like an instruction given regarding the defendant’s prerogative not to testify. The defendant said he had no objection to the giving of such an instruction.
The court used some of defense counsel’s proposals in instructing the jury, as well as the state’s, and the judge added some of his own. The defendant now argues that the preparation and giving of these instructions over his objection violated his state and federal constitutional rights to self-representation, citing Faretta v. California, 422 U.S. 806, 95 S.Ct. 2525, 45 L.Ed.2d 562 (1975). We do not agree.
Instructions of the court are just that, instructions of the court, and not the instructions of the parties. True, the parties have a right to be heard concerning the instructions to be given, to voice objections thereto, and to propose instructions to the court. The defendant was given an opportunity to do this in the instant case. But the instructions in the final analysis are the court’s, and the court may look to any source for help and assistance in preparing these instructions. Defendant’s right of self-representation does not give him the power to exclude his advisory counsel from participating in the settling of instructions.
DEATH PENALTY STATUTE ISSUES
The defendant raises four attacks on our death penalty statute’s constitutionality.
12.
The first is that applying A.R.S. § 13-703 (Arizona’s death sentence statute) violates the prohibition against cruel and unusual punishment embodied in the eighth amendment and Ariz. Const, art. 2 § 15. The defendant cites two reasons for this conclusion, the first being that the sentencing scheme invites arbitrary and capricious application of the death penalty. In support of this contention the defendant asserts that there is no stated burden of proof for a defendant’s establishment of mitigating factors, and that the notion of mitigation “sufficiently substantial to call for leniency” leaves too much to the discretion of the sentencing judge.
The defendant’s arguments here are a variation on the theme that A.R.S. § 13-703 fails to provide adequate standards to guide sentencing discretion. We have previously stated that the purpose of an aggravation/mitigation hearing is to tailor the penalty to the offender as well as the crime, and that the Arizona capital sentencing plan aims both at flexibility to permit individualized decisionmaking and at prevention of arbitrariness by creating standards to guide the sentencer. See State v. Gretzler, 135 Ariz. 42, 54, 659 P.2d 1, 13, cert. denied - U.S. -, 103 S.Ct. 2444, 77 L.Ed.2d 1327 (1983). We have described the formula of “sufficiently substantial to call for leniency” as involving the weighing of aggravating against mitigating circumstances on the basis of the gravity of each circumstance. See id. And we have grounded our independent review of whether a defendant has established a mitigating circumstance on a preponderance of the evidence standard. We believe that under these conditions we have eliminated the risk of capriciousness to the extent necessary to defeat any claim that the application of our death penalty statute constitutes cruel and unusual punishment, or in some manner violates due process.
Defendant further contends that the sentencing scheme must be unconstitutional because the prosecutor has unbridled authority in his decision whether to seek the death penalty. This contention has been previously addressed by the United States Supreme Court, which stated that pre-sentencing decisions by actors in the criminal justice system that may remove an accused from consideration for the death penalty are not unconstitutional. Gregg v. Georgia, 428 U.S. 153, 199, 96 S.Ct. 2909, 2937, 49 L.Ed.2d 859, 889 (1976). We find no merit in the defendant’s eighth amendment claims.
*29313.
The next attack on the death penalty statute advanced by the defendant is that its failure to involve a jury in the capital sentencing decision violates his sixth amendment rights. This argument has been rejected by the United States Supreme Court in Proffit v. Florida, 428 U.S. 242, 252, 96 S.Ct. 2960, 2966, 49 L.Ed.2d 913, 922-23 (1976), and has likewise been rejected by this court on numerous occasions. State v. Richmond, 137 Ariz. 312, 316, 666 P.2d 57, 61 (1983); State v. Gretzler, supra, 135 Ariz. at 56, 659 P.2d at 15 (citing cases).
14.
The third attack on A.R.S. § 13-703 is that the statute violates due process because the legislature placed the burden of proof of mitigating circumstances on the defendant. Richmond, supra, is dispositive of this claim: “[o]nce the defendant has been found guilty beyond a reasonable doubt, due process is not offended by requiring the defendant to establish mitigating circumstances.” State v. Richmond, supra, 137 Ariz. at 316, 666 P.2d at 61. Accord, State v. Smith, 125 Ariz. 412, 416, 610 P.2d 46, 50 (1980); State v. Watson, 120 Ariz. 441, 447, 586 P.2d 1253, 1259, cert. denied 440 U.S. 924, 99 S.Ct. 1254, 59 L.Ed.2d 478 (1978).
15.
The defendant’s final attack on the constitutionality of the statute is that it is impermissibly void for vagueness. This argument is directed toward the aggravating circumstance concerning murders committed in “an especially heinous, cruel or depraved manner.” A.R.S. § 13-703(F)(6). The defendant claims that it is impossible to make a finding of this circumstance with uniformity because our definitions of terms in the quoted phrase defy standardization. We disagree; as we stated in State v. Jeffers:
Each element — cruel, heinous and depraved — has been narrowly defined and construed.
* * * * * *
We have been insistent that the murder be especially cruel or especially depraved before this section would apply. We have clearly defined the terms and have delineated factors to guide us in determining if the crime was indeed committed in such a manner. State v. Gretzler, supra. State v. Jeffers, 135 Ariz. 404, 430, 661 P.2d 1105, 1131 (1983) (emphasis in original)
The best empirical evidence refuting the charge of impossibility of standardizing the “cruel, heinous or depraved” circumstance is our recent decision in State v. Richmond, supra. Though this court affirmed the defendant’s conviction and sentence in that opinion, three members of the court voted against the author’s finding that the crime was especially heinous and depraved. Id., 135 Ariz. at 421, 423, 661 P.2d at 1122, 1124 (concurring opinion of Cameron, J., and Gordon, V.C.J.; dissenting opinion of Feld-man, J.). The disagreement as to the existence of this circumstance focused on whether the record supported a finding of infliction of gratuitous violence upon, and needless mutilation of, the victim. The lengths to which this court has gone in order to insure the proper application of the definitions of terms like “cruel” and “depraved” reflect a commitment to uniformity in imposition of this most serious sanction. We believe that such efforts give sufficient guidance to sentencing courts, and that the legislatively propounded criteria for the aggravating circumstances are accordingly not impermissibly overbroad or vague.
INDEPENDENT REVIEW OF SENTENCE
We review each death penalty imposed by our state’s sentencing courts to insure that the sentence has not been applied in an arbitrary or capricious manner. We independently review the record of each capital case to determine the correctness of the findings of the trial court as to aggravating and mitigating circumstances, in order to independently determine the propriety of the sentence imposed. State v. Zaragoza, 135 Ariz. 63, 68, 659 P.2d 22, 27 (1983); *294State v. Gretzler, supra, 135 Ariz. at 57, 659 P.2d at 16.
In the instant case, the defendant was sentenced to life imprisonment, on 30 July 1981, for his conviction of dangerous or deadly assault by prisoner, A.R.S. § 13-1206. State v. Harding, Cause No. CR-04694, aff'd No. 5417, filed 29 April 1982. This felony involves commission of an assault “using or exhibiting a deadly weapon or dangerous instrument,” or the knowing or intentional infliction of “serious physical injury” on the assaulted party. A.R.S. § 13 — 1206. The facts of the prior conviction indicate the defendant and another jail inmate struck a fellow inmate several times with darts discharged through a homemade blowgun. One dart penetrated the victim’s jawbone, a second traversed his skin near the shoulder, and a third penetrated his leg. A nurse and a forensic pathologist both testified at the trial of this matter that the darts were capable of causing serious physical injury.
On these facts we find that this earlier conviction supports the finding of two aggravating circumstances: A.R.S. § 13-703(F)(1) conviction of an offense punishable in Arizona by life imprisonment; and (F)(2), conviction of a felony involving the use of violence on another person.
As to the finding that the murder was committed for pecuniary gain, the record indicates that the defendant removed clothing, a briefcase and credit cards from the possession of Robert Wise. He left the scene of the homicides in a car that had been in the custody of Martin Concannon. The instant sequence of binding, robbing and leaving helpless the victims while stealing their auto, like defendant’s earlier conduct in the Svetgoff robbery, supports a finding that the defendant committed the murders in the course of obtaining valuable personal property from his victims. We therefore find that the aggravating circumstance of A.R.S. § 13-703(F)(5) exists in the instant action.
The trial court additionally found as an aggravating circumstance that the murders were committed in “an especially cruel, heinous and depraved manner.” See A.R.S. § 13-703(F)(6). The court did not state on the record what aspects of the crimes it found to be cruel, heinous or- depraved. The medical examiner testified that some of the bindings restraining the victims were secured so tightly that they caused abrasions and black and blue discoloration of the skin resulting from hemorrhaging of tiny capillaries beneath the skin’s surface. Likewise, bludgeoning of the bodies caused abrasion, discoloration and hemorrhaging. The doctor testified, however, that such physical manifestations of blunt trauma are consistent with injuries inflicted prior to, contemporaneously with, or shortly after the time of death. He did not speculate whether the beatings of the victims occurred before or after their deaths. He stated only that Martin Con-cannon lived between 3 and 20 minutes after being shot, but it is not known whether he was conscious at the time. The investigating officers testified to the facts of Wise’s tethering by the neck to the bedpost and of Concannon’s gagging with socks, which the doctor testified obstructed his breathing passages.
The state must prove this aggravating circumstance, like the others, beyond a reasonable doubt. State v. Jordan, 126 Ariz. 283, 286, 614 P.2d 825, 828, cert. denied 449 U.S. 986, 101 S.Ct. 408, 66 L.Ed.2d 251 (1980). Because there is no evidence beyond a reasonable doubt that the victims were conscious, the state’s evidence fails to establish that this sadistic treatment was especially cruel to the victims. See State v. Gretzler, supra, 135 Ariz. at 51, 659 P.2d at 10.
The finding of depravity, however, is sustainable. The photographs of the autopsy of Robert Wise make a strong case for this finding. The right side of Wise’s face, from the area between the temple and the jaw line, was severely bruised and abraded. His right ear lobe was nearly severed, and his jaw was so broken as to have chipped off bone fragments and to have displaced the jaw from the normal *295mandibular joint position. The nature and location of the damage sustained required a number of blows to the victim’s face while the victim was stationary. The beating must have been administered while the victim was restrained, unconscious or deceased. The helplessness of the victim plus the gratuitous nature of the bludgeoning, beyond the point necessary to rob or to dispatch the victims by shooting, renders the beating apart from the usual or the norm, and it is therefore depraved. Cf. State v. Ceja, 115 Ariz. 413, 417, 565 P.2d 1274, 1278, cert. denied 434 U.S. 975, 98 S.Ct. 533, 54 L.Ed.2d 467 (1977) (barrage of violence found depraved); State v. Woratzeck, 134 Ariz. 452, 457, 657 P.2d 865, 870 (1982). Even if the beating with the lamp base occurred after the victim’s decease, we still find this to be an act of gratuitous violence and a debasement of a corpse bordering on “needless mutilation of the victim.” State v. Gretzler, supra, 135 Ariz. at 52, 659 P.2d at 11. Cf. State v. Jeffers, supra, 135 Ariz. at 430, 661 P.2d at 1131 (post-mortem beating of victim resulting in additional wounds and bleeding found especially heinous and depraved). The savage beating of Robert Wise, regardless of its timing, reflects a depraved mental state. The same is true of the treatment given Concannon, who was perversely gagged.
The defendant chose not to present any evidence in mitigation, despite the trial court’s urging. The burden of proof on mitigation is the defendant’s. A.R.S. § 13-703(C). Since the defendant did not put on evidence of mitigating circumstances, the trial court found none. We do not, on review of the record before us, find conclusive evidence tending to show mitigation of the instant sentences.1 We therefore independently find that there are no mitigating circumstances sufficiently substantial to call for leniency. The aggravating eircum-stances justify the imposition of the death penalty. See A.R.S. § 13-703(E).
PROPORTIONALITY REVIEW
This court conducts a proportionality review to determine “whether the sentences of death are excessive or disproportionate to the penalty imposed in similar cases, considering both the crime and the defendant.” State v. Richmond, 114 Ariz. 186, 196, 560 P.2d 41, 51 (1976), cert. denied 433 U.S. 915, 97 S.Ct. 2988, 53 L.Ed.2d 1101 (1977). This procedure has been endorsed by our federal circuit in Harris v. Pulley, 692 F.2d 1189, 1196 (9th Cir.1982), cert. granted sub nom. Pulley v. Harris, - U.S. -, 103 S.Ct. 1425, 75 L.Ed.2d 787 (1983).
We have considered other cases in which a defendant with a serious criminal history murdered his victims for gain and in an especially cruel, heinous or depraved manner. See State v. Gretzler, supra; State v. Raymond Tison, 129 Ariz. 546, 633 P.2d 355 (1981), cert. denied - U.S. -, 103 S.Ct. 180, 74 L.Ed.2d 147 (1982); State v. Ricky Tison, 129 Ariz. 526, 633 P.2d 335 (1981) , cert. denied - U.S. -, 103 S.Ct. 180, 74 L.Ed.2d 147 (1982); State v. Gerlaugh, 135 Ariz. 89, 659 P.2d 642 (1983), supplementing 134 Ariz. 164, 654 P.2d 800 (1982) . In the first of these comparison cases, the defendant claimed partial impairment of his capacity to appreciate the wrongfulness of his conduct. The defendants in the last three cases claimed youth as a mitigating circumstance. In the instant case, the defendant was in his thirties at the time of the murders, and put on no evidence of mental impairment. Each of the defendants in the comparison cases received the death penalty and we affirmed their sentences. We find that the affirmance of the sentence here is not dispropor*296tionate. We have searched the record for fundamental error, A.R.S. § 13-4035, and find none.
The convictions and sentences are affirmed.
HOLOHAN, C.J., and HAYS, J., concur.. In reviewing the presentence report, we take note of the following facts: the defendant was shuffled back and forth among family members at an early age; he first became institutionalized at the age of 10 for recurrent truancy; and he was diagnosed at about the age of 14 to have minimal brain damage and petit mal seizures, while his intelligence registered in the dull normal range. Despite these last factors, repeated psychological evaluations revealed no distortions in the defendant’s thinking processes and a consistent diagnosis of no psychotic manifestations. His last psychological evaluation prior to his arrest on the instant charges resulted in a diagnosis of severe antisocial personality without psychosis.