Michael Owsley was convicted of first-degree murder, kidnapping, and two counts of armed criminal action, and was sentenced to death. After unsuccessfully attempting to overturn his convictions in the Missouri state courts, Mr. Owsley petitioned for habeas corpus relief. The district court1 denied the petition and granted a certificate of appealability on two of Mr. Owsley’s claims. We affirm.
I.
Mr. Owsley claims that the state trial court violated his constitutional rights by failing to appoint substitute counsel for him. He contends first that an irreconcilable conflict arose between him and his court-appointed counsel, James McMullin, during the course of preparation for his trial. Because of this conflict, Mr. Owsley alleges that there was a complete breakdown in communications and that Mr. McMullin was thus incapable of defending him effectively. Among other things, Mr. Owsley accuses Mr. McMullin of neglecting to meet and consult with him about his defense, failing to conduct all requested investigations, speaking to him in a condescending fashion, and calling him a profane name.
When considering a habeas corpus petition, we examine the record to determine whether the relevant decision of the state courts “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court,” see 28 U.S.C. § 2254(d)(1). In doing so, we are mindful of the recent interpretation of this statute in Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), where the Supreme Court emphasized that the phrase “Federal law, as determined by the Supreme Court,” refers to “the holdings, as opposed to the dicta, of this Court’s decisions,” and cautioned that § 2254(d)(1) “restricts the source of clearly established law to this Court’s jurisprudence,” id. at 1523.
To obtain habeas relief, Mr. Owsley must therefore be able to point to a Supreme Court precedent that he thinks the Missouri state courts acted contrary to or unreasonably applied. We find that he has not met this burden in this appeal. Mr. Owsley’s claims must be rejected because he cannot provide us with any Supreme Court opinion justifying his position.
Mr. Owsley refers to a few Supreme Court decisions that, at most, deal only remotely with the issues of his case. See Holloway v. Arkansas, 435 U.S. 475, 98 S.Ct. 1173, 55 L.Ed.2d 426 (1978), and Glasser v. United States, 315 U.S. 60, 62 S.Ct. 457, 86 L.Ed. 680 (1942). These decisions concern conflicts of interest that arise when an attorney represents multiple defendants in the same case, see Holloway, 435 U.S. at 484-85, 489-90, 98 S.Ct. 1173, and Glasser, 315 U.S. at 75-76, 62 S.Ct. 457, a context that in no way resembles Mr. Owsley’s situation. These cases are therefore inapplicable to Mr. Owsley’s complaints about his personality conflicts with his counsel. Because there is no Supreme Court holding that controls the issue of Mr. Owsley’s complaint, we cannot disturb the rulings of the Missouri state courts.
Mr. Owsley also contends that his constitutional rights were violated when the state trial court refused to appoint another attorney for him for the purpose of moving for substitute counsel. During the arguments on that motion, Mr. Owsley stated his reasons for asking the trial court to replace Mr. McMullin with anoth*1058er lawyer, and Mr. McMullin disagreed, in response, with several of Mr. Owsley’s factual allegations. Mr. Owsley claims that Mr. McMullin’s contradiction of his statements effectively left him without the assistance of counsel for the purposes of that motion.
Under the sixth amendment, a criminal defendant is entitled to have the assistance of counsel for all of the critical stages of his trial. See United States v. Wade, 388 U.S. 218, 226-27, 87 S.Ct. 1926, 18 L.Ed.2d 1149 (1967). To obtain relief based on a violation of the sixth amendment right to counsel, a defendant must prove, among other things, that he suffered actual prejudice. See Strickland v. Washington, 466 U.S. 668, 691-92, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
The Missouri Supreme Court found that Mr. Owsley did not suffer any prejudice at the hearing on his motion, see State v. Owsley, 959 S.W.2d 789, 793 (Mo.1997) (en banc), cert. denied, 525 U.S. 882, 119 S.Ct. 191, 142 L.Ed.2d 156 (1998), and our examination of the record leaves us unable to say that this conclusion was unreasonable. See 28 U.S.C. § 2254(d)(2); see also Evans v. Rogerson, 223 F.3d 869, 872-73 (8th Cir.2000). Indeed, Mr. Owsley does not indicate precisely how the state trial court’s rejection of his request worked to his prejudice. We note, too, that Mr. Owsley had a full and fair opportunity to inform the trial court why he wanted someone else other than Mr. McMullin to represent him, and the record indicates that the trial court understood fully what Mr. Owsley was trying to say. This claim therefore fails.
II.
Mr. Owsley also asserts that the state trial court unconstitutionally denied him the right to introduce evidence of his intoxication from alcohol and drugs. He maintains that this evidence would have tended to show that he did not have the ability to deliberate required by the offenses for which he was charged. The trial court refused to allow Mr. Owsley to call witnesses to testify about his intoxication because of Mo.Ann.Stat. § 562.076.3, which severely limits the use .of such evidence. On appeal, the Missouri Supreme Court declined to review this ruling, holding that Mr. Owsley had failed to preserve the issue for review. See Owsley, 959 S.W.2d at 795.
We are obliged to respect the conclusion of the Missouri Supreme Court here. A federal court conducting habeas corpus review'must ordinarily refrain from reviewing any issue that a state court has already found to be defaulted on an adequate and independent state-law basis. See Murray v. Carrier, 477 U.S. 478, 488, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986); Wainwright v. Sykes, 433 U.S. 72, 90-91, 97 S.Ct. 2497, 53 L.Ed.2d 594 (1977); and Pollard v. Armontrout, 16 F.3d 295, 297 (8th Cir.1994). In Missouri, it has always been the rule that to preserve a constitutional issue for review, the issue “must be raised at the earliest time consistent with good pleading and orderly procedure,” State v. Flynn, 519 S.W.2d 10, 12 (Mo.1975); see also State v. Tygart, 673 S.W.2d 83, 87 (Mo.Ct.App.1984). Furthermore, “the sections of the Constitution claimed to have been violated must be specified; the point must be preserved in the motion for new trial, if any; and it must be adequately covered in the briefs,” Magenheim v. Board of Education, 340 S.W.2d 619, 621 (Mo.1960); see also State v. Sullivan, 935 S.W.2d 747, 754 (Mo.Ct.App.1996). It is not enough that the defendant make a vague objection to a ruling that he or she does not like, and “abstract statements of law or mere assertions” do not qualify an argument for appellate review under the Missouri rules, Magenheim, 340 S.W.2d at 621.
At trial, Mr. Owsley’s attorney responded to the court’s ruling on § 562.076.3 only by saying that he did not “agree with that” and he did not “agree with the legislature.” Mr. Owsley’s attorney did not specify why *1059he thought that the trial court’s ruling was incorrect, nor did he provide any reason for his view that the Missouri statute should not have been applied. The Missouri Supreme Court thought that counsel’s general protestations were insufficient to preserve Mr. Owsley’s appeal on the issue of the intoxication evidence, see Owsley, 959 S.W.2d at 795, and this was manifestly correct under the Missouri state courts’ rules, which have been consistently followed and do not place an unreasonable burden on the assertion of a federal right. See Ford v. Georgia, 498 U.S. 411, 423-24, 111 S.Ct. 850, 112 L.Ed.2d 935 (1991). This claim is therefore defaulted.
III.
Although the district court issued a certificate of appealability for only two of Mr. Owsley’s habeas corpus claims, he opted nonetheless to raise all of his original claims in his brief on appeal. We decline to discuss the merits of these other claims as they are not properly before us.
For the reasons indicated, we affirm the district court’s denial of Mr. Owsley’s petition.
. The Honorable Dean Whipple, United States District Judge for the Western District of Missouri.