In 2008, a jury in the Superior Court found the *490defendant guilty of unlawful possession of a firearm, in violation of G. L. c. 269, § 10 (a); and unlawful possession of a class B controlled substance, cocaine, in violation of G. L. c. 94C, § 34. As proof that the weapon the defendant possessed was a firearm and the substances found in his clothing were cocaine, the Commonwealth offered in evidence a ballistics certificate and two certificates of drug analysis. The certificates were admitted without testimony from the analysts who had prepared them, and without objection by the defendant. The defendant subsequently appealed, arguing that he was denied his right to a fair trial under the Sixth and Fourteenth Amendments to the United States Constitution because the certificates were admitted without a showing of the unavailability of the analysts or a prior opportunity to cross-examine them, in contravention of Melendez-Diaz v. Massachusetts, 557 U.S. 305 (2009). A divided panel of the Appeals Court affirmed the firearms conviction but reversed the drug conviction. Commonwealth v. Ramsey, 79 Mass. App. Ct. 724, 730-731 (2011). We granted both parties’ applications for further appellate review. Because we are satisfied that the improper admission of both the ballistics certificate and drug certificates did not contribute to the jury’s verdict, where the defendant conceded as part of his trial strategy that he possessed both the gun and cocaine and agreed that the jury be instructed that the Commonwealth had proven all elements of both charges beyond a reasonable doubt, we conclude that the certificates’ introduction at trial was harmless beyond a reasonable doubt. Accordingly, we affirm both convictions.
1. Facts. We present the essential facts the jury could have found, reserving certain details for our discussion of the issues. On January 1, 2007, Springfield police Officer Ramon Sierra and his partner responded to a shooting at a local restaurant. While traveling to the scene, Officer Sierra heard several shots fired and then saw the defendant walking “at a very fast pace . . . [with] his hands in front of his body . . . .” Despite Sierra’s order to stop, the defendant continued on, reached for something in his waistband, and then threw away an item that Sierra recognized to be a weapon. Police apprehended the defendant who, after indicating that he had been wounded, was *491transported to a hospital for treatment of injuries to his foot. The attending nurse removed what appeared to be “crack” and powder cocaine from the defendant’s sock. The substances were collected for evidence and subsequent drug analysis issued positive results for cocaine.
In the meantime, Sierra searched the area where the defendant discarded the weapon and located a semiautomatic pistol. A third police officer, who had inspected the gun, noted that it was unloaded but contained a magazine, and seized it for later assessment of its operability. The ensuing ballistics certificate showed that the pistol bore no malfunctions and could discharge a bullet. A search for other ballistics evidence uncovered several spent shell casings both inside and outside the restaurant.
At trial, a State police trooper testified as an expert witness that the recovered handgun was test fired by a colleague and that, based on comparisons the trooper personally made with test specimens, two of the cartridge casings retrieved from outside the restaurant were positively identified as having been fired from the seized weapon.
The defendant testified, admitting that he possessed both the gun and the cocaine, but raising a defense of necessity as to the firearms charge.1 He stated that, on the morning of January 1, *4922007, he was at the restaurant extending wishes for a happy New Year to acquaintances when he suddenly heard gunshots and noticed that one of his friends was hurt. After he spotted a gun lying on a nearby table, the defendant grabbed it while picking up his injured friend and dragging him outside to safety. He stated that he took the gun because he did not want someone else to pick it up and use it against him. Once outside of the restaurant, the defendant, with the gun still in his possession, left his friend on the sidewalk and started to run because he realized he had just been shot in the foot and was “scared for [his] life.”
In support of the necessity defense, defense counsel in closing argument described a chaotic scene at the restaurant, resulting in “monstrous danger” and forcing the defendant to make an automatic judgment about taking possession of the gun to prevent others from discharging it. In order to bolster the defendant’s credibility, defense counsel further argued, “[The defendant] comes before you and says, listen, I picked up a gun. I was in possession of the gun. . . . And he admits to you on the stand he had cocaine in his sock.”
Recognizing that the defendant’s entire defense strategy revolved around convincing the jury that he acted out of necessity in possessing the gun, the judge inquired prior to instructing the jury whether defense counsel preferred jury instructions that included a complete explanation of the elements of the crimes charged or instructions that simply focused on the defense of necessity. After conferring with the defendant, defense counsel stated that the defendant “concedes both possession of the gun, as well as the possession of the cocaine.”* 2 As to both charges, the judge instructed the jury in nearly identical language *493that “the parties have agreed that the Commonwealth has, in fact, satisfied beyond a reasonable doubt each and every one of these elements.” The judge instructed the jury on the application of the necessity defense as to the firearms charge only.3 Defense counsel indicated that he was satisfied with the instructions.
2. Discussion. The Commonwealth concedes, as it must, that admission in evidence of the ballistics and drug certificates without testimony of the analysts was error. Although the defendant did not object to the production of the certificates at trial, such an objection would have been futile because of our decision in Commonwealth v. Verde, 444 Mass. 279, 280, 283-284 (2005) (drug certificates may be properly introduced as business records), on which defense counsel was entitled to rely. The United States Supreme Court’s mling in Melendez-Diaz v. Massachusetts, 557 U.S. 305, 310-311 (2009) (certificates of analysis are testimonial statements whose admission in evidence compels protection of confrontation clause), which abrogated Commonwealth v. Verde, supra, was issued after the defendant’s trial. We review the error to determine whether it was harmless beyond a reasonable doubt. Commonwealth v. Vasquez, 456 Mass. 350, 352 (2010).
*494“The ‘essential question’ in analyzing harmlessness beyond a reasonable doubt is ‘whether the error had, or might have had, an effect on the [fact finder] . . . .’ ” Commonwealth v. King, 461 Mass. 354, 356 (2012), quoting Commonwealth v. Vasquez, supra at 360. In conducting the analysis, “we ask whether, on the totality of the record before us, weighing the properly admitted and the improperly admitted evidence together, we are satisfied beyond a reasonable doubt that the tainted evidence did not have an effect on the jury and did not contribute to the jury’s verdicts.” Commonwealth v. Mendes, 463 Mass. 353, 358 (2012), quoting Commonwealth v. Tyree, 455 Mass. 676, 701 (2010). An error may be considered harmless when other properly admitted evidence of guilt is so “overwhelming” as to nullify any effect that the improperly introduced evidence might have had on the outcome. Commonwealth v. Dagraca, 447 Mass. 546, 555 (2006). Additionally, “[a]n assertion [of harmless error] ... is most particularly vulnerable where the over-all strength of the Commonwealth’s case radiates from a core of tainted evidence.” Commonwealth v. Muniz, 456 Mass. 166, 169 (2010), quoting Commonwealth v. Tyree, supra at 701-702.
In evaluating whether the improper admission of evidence was harmless beyond a reasonable doubt, we examine factors such as “the importance of the evidence in the prosecution’s case; the relationship between the evidence and the premise of the defense; who introduced the issue at trial; the frequency of the reference; whether the erroneously admitted evidence was merely cumulative of properly admitted evidence; the availability or effect of curative instructions; and the weight or quantum of evidence of guilt.” Commonwealth v. Mendes, supra at 359, quoting Commonwealth v. Dagraca, supra at 553. These factors, although useful, “are not exclusive or exhaustive.” Commonwealth v. Mahdi, 388 Mass. 679, 697 (1983).
a. Drug certificates. As to the drug certificates, there is no doubt that they are powerful evidence of the identity of an alleged illegal substance, and their improper admission will not be easily overcome. See Commonwealth v. Vasquez, supra at 363-364. Drug certificates “assure the fact finder, to a degree that virtually no amount of circumstantial evidence can, that the charged substance is in fact a particular illegal drug.” Id. *495Ultimately, however, when conducting a harmless error analysis, our focus is “whether, on the totality of the record before us, . . . we are satisfied beyond a reasonable doubt that the tainted evidence did not have an effect on the jury and did not contribute to the jury’s verdicts.” Commonwealth v. Mendes, supra at 358, quoting Commonwealth v. Tyree, supra at 701. To be sure, the “defendant’s theory of his case cannot [by itself] relieve the Commonwealth of its burden of proving every element of a crime.” See Commonwealth v. Shea, 398 Mass. 264, 269 (1986). However, the Commonwealth may be relieved of that burden where the defendant stipulates to the identity of a substance as an illegal drug. See Commonwealth v. Ortiz, ante 475, 481 (2013); Commonwealth v. Charles, 456 Mass. 378, 383 (2010); Commonwealth v. Muniz, supra at 173 n.7.
Because the defendant was indicted for unlawful possession of a firearm after having been previously convicted of three violent crimes, he faced a sentence of from fifteen to twenty years’ imprisonment if convicted. G. L. c. 269, § 10G (c).4 *In contrast, the charge for simple possession of cocaine carried a maximum sentence of one year. G. L. c. 94C, § 34.5 With this disparity in mind, the defendant apparently made the strategic decision to concede the possession of cocaine charge in order to boost his credibility with the jury in the hopes they might credit his defense of necessity to the firearms charge.6
*496This is not a case where the defendant merely failed to contest that the substances were drugs or where defense counsel arguably conceded the nature of the substances by simply referring to them as “drugs” or “cocaine” and encouraging the jury to return a verdict of guilty on a lesser included offense of simple possession. See Commonwealth v. Charles, supra. See also Commonwealth v. Fluellen, 456 Mass. 517, 526-527 (2010); Commonwealth v. Muniz, supra. We remain of the view that a concession of this variety — essentially a failure to contest the issue — does not constitute a tacit stipulation to the identity of a substance as an illegal drug, and that, without more, such a concession does not render the improper admission of a drug certificate harmless. See Commonwealth v. Charles, supra.
Here, in contrast, the defendant took the stand and unequivocally admitted to possessing both crack and powder cocaine. More importantly, however, the jury were told, with the defendant’s consent, see note 2, supra, that the parties agreed the substance was cocaine and that they (the jury) need not consider the issue. Regardless of whether the defendant’s concession on the identity of the substance constituted a “stipulation” in the formal sense, or whether it technically relieved the Commonwealth of its burden of proof, the impact it had on the jury’s verdict is unmistakable. See Commonwealth v. Ramsey, 79 Mass. App. Ct. 724, 734-735 (2011) (Grasso, J., dissenting). We are thus satisfied that the drug certificates did not contribute to the jury’s verdict, and conclude that their improper admission was harmless beyond a reasonable doubt.7,8
b. Ballistics certificate. In order for the defendant to be *497convicted of unlawful possession of a firearm, the Commonwealth must demonstrate that the weapon he possessed met the legal definition of a firearm under G. L. c. 140, § 121, including that the weapon was operable. See Commonwealth v. Muniz, 456 Mass. 166, 169 (2010). “The Commonwealth’s burden to prove that a weapon is a ‘firearm’ in the statutory sense is not a heavy one.” Commonwealth v. Loadholt, 456 Mass. 411, 430-431 (2010), S.C., 460 Mass. 723 (2011). Proving this element beyond a reasonable doubt “requires only that the Commonwealth present some competent evidence from which the jury reasonably can draw inferences that the weapon will fire . . .” (emphasis in original). Commonwealth v. Loadholt, supra at 431, quoting Commonwealth v. Nieves, 43 Mass. App. Ct. 1, 2 (1997).
The defendant disputes the sufficiency of the properly admitted evidence to prove that the gun had been fired or was otherwise operable. Specifically, he asserts that, even though he conceded through his trial strategy that he possessed the gun, the “defense by itself did not amount to a concession regarding the functionality of the gun.” This argument misses the point. It is true that the defendant’s testimony conceded only that the defendant possessed the gun, and did not speak to the gun’s operability. However, as with the drug charge, defense counsel, after conferring with the defendant, made the strategic decision to eliminate all potential distractions from the purview of the jury so that they could focus solely on evaluating the defendant’s necessity defense. In doing so, he agreed that the judge could explain to the jury that none of the elements of the firearms charge was in dispute, meaning that he agreed that the gun he possessed met the legal definition of a firearm. Indeed, as agreed in his earlier *498conversation with the parties at the charge conference, the judge did not even instruct the jury on the legal definition of a firearm or the effect of the ballistics certificate. Apart from merely listing the elements of the firearms charge, the judge elaborated only on the defense of necessity, and instructed that in order to convict the defendant, the jury must find that the Commonwealth proved beyond a reasonable doubt that the defendant did not act out of necessity. Accordingly, as with the drug certificates, we are satisfied that the ballistics certificate did not contribute to the jury’s verdict.9
Judgment affirmed.
Regarding the defendant’s possession of cocaine, the following exchange occurred between the prosecutor and the defendant:
The prosecutor: “And . . . when the nurse was working on you, they took your sock off and you had these items in your sock; correct?”
The defendant: “Yes, sir.”
The prosecutor: “Right there, is that in your left sock? I am showing you Exhibit 4A, was this in your left sock?”
The defendant: “Yes, sir.”
The prosecutor: “That is crack cocaine?”
The defendant: “Yes, sir.”
The prosecutor: “And I am showing you Exhibit 4. That is some powder cocaine that was in your left sock?”
The defendant: “Yes, sir.”
The prosecutor: “And that was in your possession when you went to the hospital?”
*492The defendant: “Yes, sir.”
The prosecutor: “And the nurses took it away from you and gave it to the Springfield police; correct?”
The defendant: “Yes, sir.”
The entire exchange reads as follows:
The Judge: “The defendant seemed to concede in his closing argument possession of a weapon and possession of drugs; what do you want me to instruct the jury? Do you want me to go through the whole instruction or simply focus on the issue you raised, and that is necessity?”
*493Defense counsel: “I think you should go through all the elements.”
The Judge: “Constructive possession and actual, I mean the whole nine yards, the certificate, things like that?”
Defense counsel: “May I have one moment, Judge?”
The Judge: “Sure.”
Defense counsel: “After discussion with [the defendant], we would ask that your focus be on the necessity.”
The Judge: “Okay."
Defense counsel: “He concedes both possession of the gun, as well as the possession of the cocaine.”
The Judge: “What I can simply do is read the elements and indicate that they are not an issue, and the issue is simply necessity, for both the drugs and the firearm.”
Defense counsel: “That is correct.”
Although the judge initially indicated he would instruct on the necessity defense as to both the firearms and drug possession charges, at no time did the defendant present any defense to the drug possession charge.
The trial was bifurcated, and following the jury trial on the underlying firearms charge and drug possession charge, the defendant pleaded guilty to so much of the subsequent offender portion of the indictment as charged a violation of G. L. c. 269, § 10G (a). Section 10G (a) carries a sentence of three to fifteen years’ imprisonment. The defendant was sentenced to a term of imprisonment of from eight to ten years on this indictment.
Although the indictment charged unlawful possession of cocaine with intent to distribute, in violation of G. L. c. 94C, § 32A (c), the defendant was tried only for the lesser included offense of possession of cocaine0.
Our case law is replete with examples of defendants who conceded guilt to lesser crimes seemingly in order to increase the likelihood of acquittal on more serious charges. See, e.g., Commonwealth v. Slazchta, 463 Mass. 37, 37 (2012) (defendant conceded guilt of murder, challenging only whether murder was in first degree or in second degree); Commonwealth v. Dargon, 457 Mass. 387, 398 (2010) (defendant stipulated to assaulting victim but denied it was sexual); Commonwealth v. Berendson, 73 Mass. App. Ct. 395, 397 (2008) (defendant admitted to robbery, attempted robbery, and choking and beating one victim, but denied sexual assaults).
The defendant argues on appeal that his decision to concede the identity of the substances as cocaine was based, at least in part, on the Commonwealth’s improper admission of the drug certificates in evidence. This court already has rejected the argument that we should consider, as part of our harmless error analysis in this type of case, what effect an improperly admitted certificate might have had on a defendant’s trial strategy. Commonwealth v. Mendes, 463 Mass. 353, 362-364 (2012) (defendant’s testimony considered only as part of totality of record).
The defendant does not argue on appeal that his concession was not made intelligently or voluntarily or that his attorney rendered ineffective assistance of counsel. His sole claim is that the improper admission of the certificates was not harmless beyond a reasonable doubt. Therefore, we need not consider, as the Appeals Court did, whether the defendant’s concession must be disregarded because it constituted an admission to all the elements of the *497crime and thus entitled the defendant to a plea colloquy he did not receive. See Commonwealth v. Ramsey, 79 Mass. App. Ct. 724, 730 n.9 (2011). The cases cited by the Appeals Court requiring plea colloquies where a defendant has admitted to sufficient facts for a finding of guilt all concern defendants who have submitted to jury-waived trials on stipulated facts, a procedure that is genuinely akin to the entry of a guilty plea except that it preserves the right to appeal certain pretrial rulings. See id., citing Commonwealth v. Castillo, 66 Mass. App. Ct. 34, 35, 37 (2006); Commonwealth v. Brown, 55 Mass. App. Ct. 440, 447-449 (2002); Commonwealth v. Hill, 20 Mass. App. Ct. 130, 132 (1985). They have no application here, where the case was tried to a jury and the defendant made the concession as part of a litigation strategy to boost his credibility with that jury. See Commonwealth v. Ramsey, supra at 735 (Grasso, J., dissenting).
Even had the defendant not agreed that the Commonwealth had met its burden of proof as to the gun’s operability, the properly admitted evidence of that operability was sufficient to overcome any harm caused by the improper admission of the ballistics certificate. Although the State trooper who testified as an expert witness on ballistics did not personally test fire the gun, he obtained information about the weapon’s rifling system by examining it. He later identified the gun as a Jennings nine millimeter caliber pistol. After giving a detailed explanation of the study and practice of firearms classification, he explained his comparison of test-fired samples with spent casings found on the sidewalk outside the restaurant. The trooper determined that two of the retrieved casings were discharged from the recovered Jennings pistol. This independent expert testimony supported the inference not only that the gun was capable of discharging a bullet, but also that it must have been fired in the vicinity of the sidewalk. See Commonwealth v. Depina, 456 Mass. 238, 250 (2010) (evidence of spent casing found in gun rendered improper admission of ballistics certificate harmless); Commonwealth v. Pittman, 76 Mass. App. Ct. 905, 907 (2010) (where officer identified spent casing as one returned to police after ballistics testing was performed on gun — even though he did not personally check weapon — his testimony regarding ballistics analysis allowed jury to infer that gun fired when tested).
This case differs from Commonwealth v. Barbosa, 461 Mass. 431, 432-433, 436-437 (2012), in which we ruled that the improperly introduced evidence was not harmless beyond a reasonable doubt because one trooper’s statement that the gun looked “authentic” did not bear on the issue of operability, and a second trooper’s testimony that the revolver had been test fired and revealed no malfunctions was based on his reading of the ballistics certificate itself. See Commonwealth v. Muniz, 456 Mass. 166, 171-172 (2010) (testimony of officer that weapon appeared in “good condition, had a round in the chamber, and was ‘ready to be fired’ ” insufficient for court to conclude that jury did not rely on certificate to prove operability). Here, the Commonwealth’s case did not “radiatef] from a core of tainted evidence,” id. at 169, quoting Commonwealth v. Tyree, 455 Mass. 676, 702 (2010), and other properly admitted corroboration was overwhelming enough to nullify any effect that the ballistics certificate may have had on the jury.