
866 S.W.2d 304 (1993)
Heriberto DELRIO, Appellant,
v.
The STATE of Texas, Appellee.
No. C14-90-00663-CR.
Court of Appeals of Texas, Houston (14th Dist.).
October 28, 1993.
Discretionary Review Refused February 16, 1994.
James M. Leitner, Houston, for appellant.
Carmen Falls Hunter, Houston, for appellee.
*305 Before MURPHY, SEARS and DRAUGHN, JJ.

OPINION ON REMAND
DRAUGHN, Justice.
This case was originally decided by this court in Delrio v. State, 820 S.W.2d 29 (Tex. App.Houston [14th Dist.] 1991, pet. granted). A jury found appellant guilty of possession of cocaine with intent to deliver, and sentenced him to life imprisonment and a $500,000.00 fine. In our original opinion, we reversed appellant's conviction on the grounds that appellant's trial counsel was ineffective in failing to challenge for cause an admittedly biased venireman's right to serve on the jury. The Court of Criminal Appeals, in a per curiam opinion, with one judge dissenting, reversed that decision and remanded the case to this court for consideration of appellant's remaining four points of error. The Court of Criminal Appeals held that the conduct of appellant's counsel in failing to challenge a venireman was not constitutionally ineffective, because the attorney may have had some viable trial strategy for keeping an admittedly biased former narcotics officer on the jury to determine his client's legal fate in the trial of a felony drug charge. See Delrio v. State, 840 S.W.2d 443, 445 (Tex.Crim.App.1992). In light of the decision by the Court of Criminal Appeals, we now address appellant's remaining points of error, and affirm the judgment of the trial court.
In point of error one, appellant contends that the trial judge committed reversible error in failing to sua sponte dismiss the prospective juror who admitted personal bias against the defendant and an inability to be impartial and fair. In our previous opinion, we suggested that the trial judge may have been obligated to dismiss an admittedly prejudiced juror in order to ensure a fair and impartial trial. See Delrio v. State, 820 S.W.2d at 32. However, in light of the opinion of the Court of Criminal Appeals, we must hold that in the absence of a challenge by appellant's counsel, the trial court did not err in allowing the admittedly biased venireman to serve on the jury. Delrio v. State, 840 S.W.2d at 445-446. Accordingly, point of error one is overruled.
In point of error three, appellant claims that he was denied due process, due course of law, and his right to compulsory process of witnesses as guaranteed by the U.S. and Texas Constitutions. Specifically, appellant alleges that he was denied his constitutional rights when the trial court allowed defense witness, Jesus Delrio, to claim a Fifth Amendment privilege to avoid testifying in the trial.
At trial, the confidential informant, who testified against appellant, stated that he knew that appellant would be present at the prearranged drug transaction because of what he was told by co-defendant Jesus Delrio ("Jesus"). Appellant was aware of this testimony prior to trial, and intended to call Jesus as a defense witness to contradict this damaging testimony which potentially illustrated his involvement in the crime. Jesus had previously pled guilty to the same offense, and had waived appeal.
When appellant called Jesus to testify, Jesus asked the court if he might be allowed to inquire about his own case. The court refused the request at that point, but informed Jesus that he was entitled to have an attorney appointed to advise him as to whether or not he should testify. After consulting with his attorney, Jesus, outside the presence of the jury, informed the court that he wanted to exercise his Fifth Amendment right not to testify on the grounds it might incriminate him. The trial court granted this request and refused to require Jesus to testify at appellant's trial.
Appellant asserts that Jesus waived his Fifth Amendment right when he pled guilty to the same offense. See Washington v. State, 388 U.S. 14, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967); Anderson v. State, 717 S.W.2d 622 (Tex.Crim.App.1986). Essentially, appellant contends that once a co-defendant pleads guilty, and fails to assert his right to appeal, he loses his right not to testify in that case because he cannot further incriminate himself, since he has already admitted his guilt. While this general rule holds true in certain *306 circumstances, it does not apply to this companion case.
An individual's constitutional privilege against self-incrimination overrides a defendant's constitutional right to compulsory process of witnesses. Bridge v. State, 726 S.W.2d 558, 567 (Tex.Crim.App.1986). We have recently reaffirmed this principle in Reese v. State, 846 S.W.2d 437, 440 (Tex. App.Houston [14th Dist.] 1992, pet. granted). Furthermore, in light of the particular facts of this case, we cannot accept appellant's argument that Jesus is not subject to further incrimination. Even when a co-defendant has pled guilty and has been sentenced in connection with the offense, he may still properly invoke his privilege against self-incrimination, because if his testimony contradicted any previous judicial admissions, he could be subject to a charge of perjury. Chandler v. State, 744 S.W.2d 341, 342-343 (Tex.App.Austin 1988, no pet.). Therefore, based on the record before us, we cannot say that the trial court committed reversible error in allowing Jesus to claim his Fifth Amendment right not to testify. Point of error three is overruled.
Continuing in this same vein, appellant in points of error four and five complains that he was denied ineffective assistance of counsel in his lawyer's failure to object to the trial court's ruling that Jesus be allowed to claim his Fifth Amendment privilege, and in the totality of his lawyer's representation of him.
With regard to his counsel's failure to object to Jesus claiming his Fifth Amendment right, we hold that this point is moot in light of our preceding discussion regarding Jesus' constitutional right not to testify. If it was not error for the trial court to permit Jesus to claim his Fifth Amendment privilege, then appellant's counsel cannot be penalized for failing to object to the court's ruling.
Aside from our previous rejected opinion concerning his failure to challenge the admittedly biased venireman during voir dire, we do not find that counsel's remaining performance was so ineffective as to have prejudiced the defense and thereby affected the outcome of the trial. Strickland v. Washington, 466 U.S. 668, 695, 104 S.Ct. 2052, 2068, 80 L.Ed.2d 674 (1984). Accordingly, points of error four and five are overruled.
The judgment of the trial court is affirmed.
