
567 N.W.2d 149 (1997)
252 Neb. 935
STATE of Nebraska, Appellee,
v.
Jeff BOPPRE, Appellant.
No. S-96-309.
Supreme Court of Nebraska.
August 1, 1997.
*151 Lawrence G. Whelan, Omaha, for Appellant.
Don Stenberg, Attorney General, and Mark D. Starr for Appellee.
WHITE, C.J., CAPORALE, WRIGHT, CONNOLLY, and GERRARD, JJ., and BURKHARD and CASSEL, District Judges.
*152 GERRARD, Justice.

INTRODUCTION
On March 13, 1989, the defendant-appellant, Jeff Boppre, was convicted, inter alia, of two counts of first degree murder for the deaths of Richard Valdez and Sharon Condon. On August 17, 1995, Boppre filed an initial motion for postconviction relief. Thereafter, on January 25, 1996, Boppre filed a second amended motion for postconviction relief, which hereinafter will be referred to as "the motion for postconviction relief." The district court overruled this motion without an evidentiary hearing. Boppre's motion for appointment of counsel for appeal of the ruling on the motion for postconviction relief was also denied. It is from these orders that Boppre timely appeals and argues, for a third time in this court, that he should be granted a new trial. Because we determine that the district court did not err in any respect, we affirm.

FACTUAL BACKGROUND
Pursuant to verdicts, Boppre was adjudged guilty of two charges of first degree murder in violation of Neb.Rev.Stat. § 28-303 (Reissue 1995), two charges of robbery in violation of Neb.Rev.Stat. § 28-324(1) (Reissue 1995), and two charges of using a firearm to commit a felony in violation of Neb.Rev.Stat. § 28-1205(1) (Reissue 1989). These charges arose out of the murders of Valdez and Condon on September 20, 1988. Boppre was sentenced to consecutive life terms of imprisonment on the murder convictions; to concurrent terms of 8 to 15 years' imprisonment on the robbery convictions; and to 6 2/3 to 20 years' imprisonment on each of the use of a firearm convictions, to be served consecutively to the other sentences. Boppre's direct appeal was heard by this court, and his convictions were affirmed in State v. Boppre, 234 Neb. 922, 453 N.W.2d 406 (1990) (Boppre I). Boppre then appealed from the district court's denial of a later motion for new trial on the basis of newly discovered evidence. We affirmed the denial of that motion in State v. Boppre, 243 Neb. 908, 503 N.W.2d 526 (1993) (Boppre II).
The facts underlying Boppre's convictions as adduced at trial are contained in Boppre I and are not repeated herein, except as otherwise indicated. Two key witnesses against Boppre were Alan Niemann and Kenard Wasmer, who testified as to the events of the night of September 20, 1988, and who accompanied Boppre to Arizona following the murders. Niemann testified that he was present at the Valdez residence at the time Boppre murdered Valdez and Condon. Wasmer also testified against Boppre. However, Wasmer maintained that he had not been present at the Valdez residence on the night of the murders.
Boppre filed a motion for postconviction relief in the instant cause, and, upon request, counsel was appointed to represent him on this motion in district court. In his motion for postconviction relief, Boppre alleged that he was denied effective assistance of counsel at trial because his trial counsel failed to develop the theory that it was Wasmer who murdered Valdez and Condon, as indicated by a pair of blue jeans that contained Condon's blood and enzyme type that were found in the trailer shared by Niemann and Wasmer and which fit the body structure of Wasmer. Boppre urges that this evidence places Wasmer at the scene, even though Wasmer claimed not to have been there. In addition, Boppre alleges that trial counsel failed to adequately examine and have tested grease stains found on the jeans to determine whether they matched the grease in which Valdez' alleged dying declaration was written. Accordingly, Boppre alleges that his trial counsel failed to adequately cross-examine witnesses, specifically Wasmer and Niemann, as to the stained jeans.
Boppre's motion was supported by the affidavit of Boppre's trial counsel, Leonard Tabor. Tabor's affidavit states that he remembers viewing the jeans during discovery and that he knew the jeans were found in the Wasmer/Niemann trailer, but that he was only recently informed that the jeans would have potentially fit the body structure of Wasmer rather than that of Boppre or Niemann. The affidavit states that until Tabor became aware that the jeans would potentially fit Wasmer, rather than Boppre or *153 Niemann, Tabor had not made the connection between the jeans and Condon's blood type. The affidavit states further that had Tabor made these connections, he would have used the evidence at trial to cross-examine Wasmer and Niemann and that his failure to do so was not part of his strategy at trial.
The district court denied Boppre's motion for postconviction relief without an evidentiary hearing. The district court found that trial counsel did pursue other theories of defense, including that either Wasmer or Niemann was the killer. In addition, the district court denied Boppre's motion for appointment of counsel to represent him in the appeal of this ruling. Boppre appeals both the denial of the postconviction motion without an evidentiary hearing and the denial of appointed counsel for the appeal.

SCOPE OF REVIEW
A criminal defendant requesting postconviction relief has the burden of establishing a basis for such relief, and the findings of the district court will not be disturbed unless they are clearly erroneous. State v. Massey, 252 Neb. 426, 562 N.W.2d 542 (1997); State v. Randall, 249 Neb. 718, 545 N.W.2d 94 (1996).
Failure to appoint counsel in postconviction proceedings is not error in the absence of an abuse of discretion. State v. Livingston, 244 Neb. 757, 509 N.W.2d 205 (1993).

ASSIGNMENTS OF ERROR
Boppre asserts that the district court erred in (1) not granting an evidentiary hearing on his motion for postconviction relief, (2) not granting him a new trial on his motion for postconviction relief, (3) not appointing counsel to represent him on appeal of the overruling of the postconviction motion, and (4) using terminology that evinced bias and prejudice toward Boppre, thereby denying him due process of law.

ANALYSIS

INEFFECTIVE ASSISTANCE OF COUNSEL
Boppre first asserts that the district court erred in not granting an evidentiary hearing on his motion for postconviction relief and in not granting him a new trial on his motion for post conviction relief. Boppre contends that failure to use the blood-stained jeans to impeach Wasmer and as evidence of Wasmer's complicity was prejudicial error. In response, the State contends that there was substantial direct and circumstantial evidence against Boppre presented at trial and that implicating Wasmer in the killings would not exculpate Boppre. In order to resolve this issue, we must determine whether the failure of Boppre's trial counsel to identify the significance of the blood-stained jeans and to introduce the jeans at trial resulted in prejudice to Boppre.
A defendant moving for postconviction relief must allege facts which, if proved, constitute a denial or violation of his or her rights under the Nebraska or U.S. Constitution. State v. Massey, supra; State v. Parmar, 249 Neb. 462, 544 N.W.2d 102 (1996). Boppre asserts that his Sixth Amendment right to effective assistance of counsel has been violated.
To sustain a claim of ineffective assistance of counsel as a violation of the Sixth Amendment to the U.S. Constitution and article I, § 11, of the Nebraska Constitution and thereby obtain reversal of a defendant's conviction, the defendant must show that (1) counsel's performance was deficient and (2) such deficient performance prejudiced the defendant, that is, demonstrate a reasonable probability that but for counsel's deficient performance, the result of the proceeding would have been different. Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984); State v. Massey, supra; State v. Schoonmaker, 249 Neb. 330, 543 N.W.2d 194 (1996). Because there was no evidentiary hearing, we examine Boppre's allegations to determine whether he alleges facts which, if proved, establish these elements.
The two prongs of the Strickland test may be addressed in either order. If it is easier to dispose of an ineffectiveness claim on the ground of lack of sufficient *154 prejudice, that course should be followed. Strickland v. Washington, supra; State v. Schoonmaker, supra.
Thus, we will initially analyze the second prong of the Strickland test, which requires the defendant to make a showing of how he was prejudiced in the defense of his case as a result of his counsel's actions or inactions. State v. Russell, 248 Neb. 723, 539 N.W.2d 8 (1995). The appellant in a postconviction proceeding has the burden of alleging and proving that the claimed error is prejudicial. State v. Randall, 249 Neb. 718, 545 N.W.2d 94 (1996); State v. Hall, 249 Neb. 376, 543 N.W.2d 462 (1996).
It is not enough for the defendant to show that the errors had some conceivable effect on the outcome of the proceeding. Virtually every act or omission of counsel would meet that test ... and not every error that conceivably could have influenced the outcome undermines the reliability of the result of the proceeding.
(Citation omitted.) Strickland v. Washington, 466 U.S. at 693, 104 S.Ct. at 2067-68.
The defendant must demonstrate a reasonable probability that but for counsel's deficient performance, the result of the proceeding would have been different. Strickland v. Washington, supra; State v. Massey, 252 Neb. 426, 562 N.W.2d 542 (1997); State v. Schoonmaker, supra. A reasonable probability is a probability sufficient to undermine the confidence in the outcome. Strickland v. Washington, supra; State v. Sims, 244 Neb. 771, 509 N.W.2d 6 (1993). The U.S. Supreme Court in Strickland stated that
[i]n making this determination, a court hearing an ineffectiveness claim must consider the totality of the evidence before the judge or jury. Some of the factual findings will have been unaffected by the errors, and factual findings that were affected will have been affected in different ways. Some errors will have had a pervasive effect on the inferences to be drawn from the evidence, altering the entire evidentiary picture, and some will have had an isolated, trivial effect. Moreover, a verdict or conclusion only weakly supported by the record is more likely to have been affected by errors than one with overwhelming record support. Taking the unaffected findings as a given, and taking due account of the effect of the errors on the remaining findings, a court making the prejudice inquiry must ask if the defendant has met the burden of showing that the decision reached would reasonably likely have been different absent the errors.
(Emphasis supplied.) 466 U.S. at 695-96, 104 S.Ct. at 2068-69.
For the purposes of our analysis, we assume that Boppre could prove that the subject jeans would have fit Wasmer, and would not have fit Boppre or Niemann, and that the jeans were found in the Wasmer/Niemann trailer. Boppre argues that the jeans would have been useful to (1) implicate Wasmer by placing him at the scene and (2) impeach Wasmer and Niemann because both testified that Wasmer had not been at the scene. Thus, Boppre contends that trial counsel ought to have cross-examined Wasmer and Niemann about the jeans and ought to have introduced the jeans into evidence. However, while placing Wasmer at the scene would have been instrumental in showing that Wasmer was more involved in the events of the night of September 20, 1988, than he has admitted, it does not make it less probable that Boppre was involved as well.
While Wasmer and Niemann were important witnesses against Boppre, they were not the sole sources of incriminating evidence. There is evidence that Boppre had previously sought to kill Valdez. Ricky Zogg testified that approximately 2 months prior to the killings, Boppre had suggested that they kill Valdez and take his money and drugs. Zogg testified that he and Boppre had attempted to kill Valdez on two prior occasions. In addition, Boppre's gun was used in the murders. A firearms expert testified that bullets recovered at the crime scene and at the Boppre residence were fired from Boppre's gun, which was recovered along the route which the three men took to Arizona.
Writings that were introduced as Valdez' dying declarations incriminated Boppre. The letters "J-F-F B-O-P-E" were written in white grease on the floor and the letters "J-E-F-F" were written on the casement of *155 the door. Both of these writings were near where Valdez' body was found. Further, Boppre was in possession of a large sum of money shortly after the date of the murders. While Boppre had made only a few small withdrawals from an automatic teller machine on the night of September 20, 1988, he was able to pay for most of the expenses on the trip to Arizona, and Boppre's friend, Cassi Bosworth, testified that upon arrival in Arizona, Boppre possessed approximately $700 to $800 in cash. Finally, Michael Neu, a fellow prisoner of Boppre's, testified as to incriminating statements that Boppre allegedly made to him.
Accordingly, in the instant case, there is other evidence sufficient that it cannot be said, to a reasonable probability, that the result would have been different had defense counsel used the jeans to impeach Niemann and Wasmer and to implicate Wasmer. The "`prejudice' component of the Strickland test ... focuses on the question whether counsel's deficient performance renders the result of the trial unreliable or the proceeding fundamentally unfair." Lockhart v. Fretwell, 506 U.S. 364, 372, 113 S.Ct. 838, 844, 122 L.Ed.2d 180 (1993). Given the weight of the evidence against Boppre and the inconclusive manner in which the jeans would have been useful to his defense, it cannot be said that the trial was unreliable or fundamentally unfair.
An evidentiary hearing on a motion for postconviction relief is required on an appropriate motion containing factual allegations which, if proved, constitute an infringement of the movant's rights under the Nebraska or federal Constitution. State v. Parmar, 249 Neb. 462, 544 N.W.2d 102 (1996); State v. Russell, 248 Neb. 723, 539 N.W.2d 8 (1995). However, a court is not required to grant an evidentiary hearing on a motion for postconviction relief which alleges only conclusions of law or fact; nor is an evidentiary hearing required under the Nebraska Postconviction Act when (1) the motion for postconviction relief does not contain sufficient factual allegations concerning a denial or violation of constitutional rights affecting the judgment against the movant, or (2) notwithstanding proper pleadings of facts in a motion for postconviction relief, the files and records in the movant's case do not show a denial or violation of the movant's constitutional rights causing the judgment against the movant to be void or voidable. State v. Schoonmaker, 249 Neb. 330, 543 N.W.2d 194 (1996); State v. Russell, 239 Neb. 979, 479 N.W.2d 798 (1992). The files and records do not show a denial of Boppre's constitutional rights because, even taking the facts as he asserts them, Boppre has not proved that he was prejudiced by any alleged deficiencies in his trial counsel's performance. Because we determine that Boppre was not sufficiently prejudiced in this matter, we do not address whether his trial counsel's performance was, in fact, deficient.
For the foregoing reasons, we conclude that the district court did not err in denying Boppre an evidentiary hearing. We further conclude that the district court did not err in overruling Boppre's motion for postconviction relief and, consequently, in denying him a new trial.

APPOINTMENT OF COUNSEL
Boppre next asserts that the district court erred in not appointing counsel to represent him on this appeal regarding the overruling of his motion for postconviction relief.
Under the Nebraska Postconviction Act, it is within the discretion of the trial court as to whether counsel shall be appointed to represent the defendant. State v. Parmar, supra; State v. Russell, 248 Neb. 723, 539 N.W.2d 8 (1995). See, also, Neb.Rev. Stat. § 29-3004 (Reissue 1995).
We have held that where the defendant's petition presented a justiciable issue to the district court for postconviction determination, an indigent defendant is entitled to the appointment of counsel. State v. Wiley, 228 Neb. 608, 423 N.W.2d 477 (1988). Conversely, we have held that where the assigned errors in the postconviction petition before the district court were either procedurally barred or without merit, establishing that the postconviction action contained no justiciable issue of law or fact, it is not an abuse of discretion to fail to appoint appellate counsel for an indigent defendant.' State v. Victor, 242 Neb. 306, 494 N.W.2d 565 (1993).
*156 In the instant case, Boppre was appointed counsel to assist him on his postconviction motion in the district court. Further, because the postconviction motion before the district court did not establish that Boppre was prejudiced by alleged ineffective assistance of counsel, it failed to present a justiciable issue of law or fact to the court. Under such circumstances, we conclude that the district court did not abuse its discretion in refusing to appoint counsel for the appeal of the denial of the postconviction motion in the case at bar.

JUDICIAL BIAS
Finally, Boppre asserts that the district court used language in its orders of February 21, 1996, and March 26, 1996, that evidenced bias and a negative disposition toward Boppre. Specifically, Boppre contends that the court's reference to him as a "convict" throughout the orders was derogatory and disrespectful and gave the appearance of bias. Boppre asserts that the trial judge should have, therefore, recused himself from the case.
A defendant seeking to disqualify a judge on the basis of bias or prejudice bears the heavy burden of overcoming the presumption of judicial impartiality. State v. Richter, 240 Neb. 913, 485 N.W.2d 201 (1992). Boppre has not met this burden in the instant case. The Nebraska Postconviction Act, Neb.Rev.Stat. § 29-3001 et seq. (Reissue 1995), refers to the individual seeking postconviction relief as a "prisoner in custody" and as "the prisoner." Black's Law Dictionary 333 (6th ed. 1990) defines a "convict" as "[o]ne who has been adjudged guilty of a crime and is serving a sentence as a result of such conviction. A prisoner." The district court's use of either the word "convict" or "prisoner" accurately described Boppre and his statutory status at the time that his motion was filed. Indeed, this court has, in the past, referred to Boppre as a "convict." See Boppre II.
Consequently, the district court's use of the term "convict" in this context, without other evidence of bias or prejudice, does not overcome the presumption of impartiality and does not evince due process concerns. This assignment of error is without merit.

CONCLUSION
Finding no merit in any of Boppre's assigned errors, we affirm the judgment of the district court.
AFFIRMED.
