
758 N.W.2d 22 (2008)
276 Neb. 818
STATE of Nebraska, Appellee,
v.
Jay D. AMAYA, Appellant.
No. S-07-1117.
Supreme Court of Nebraska.
December 5, 2008.
*24 Scott H. Trusdale, of Trusdale & Trusdale, P.C., L.L.O., Cozad, for appellant.
Jon Bruning, Attorney General, and George R. Love, Columbus, for appellee.
HEAVICAN, C.J., WRIGHT, CONNOLLY, GERRARD, STEPHAN, McCORMACK, and MILLER-LERMAN, JJ.
*25 STEPHAN, J.
In 1998, Sheri Fhuere was sexually assaulted and killed in her home in North Platte, Nebraska. Michael E. Long and Jay D. Amaya were arrested and charged in connection with the crimes. Amaya entered pleas of no contest and was convicted on one count of first degree murder, one count of use of a knife in the commission of a felony, and one count of sexual assault. The district court for Lincoln County imposed consecutive sentences of life imprisonment on the murder conviction, 10 to 20 years' imprisonment on the weapon conviction, and 20 to 40 years' imprisonment on the sexual assault conviction. No direct appeal was filed. In 2006, Amaya filed a verified motion for postconviction relief. After appointing counsel and conducting an evidentiary hearing, the district court denied postconviction relief. Amaya appeals from that order.

BACKGROUND
When police arrived at Fhuere's home on July 16, 1998, they found Long attempting to resuscitate her. Fhuere had been beaten and sexually assaulted, and her throat had been slashed. There was a severe bite mark on her left thigh. Fhuere was pronounced dead at the scene, and a pathologist later determined that she died as the result of either the slash wound or the beating.
Long was interviewed several times over the next hours and eventually gave a written statement to police dated July 16, 1998. Although there were inconsistencies in his story, he generally told officers that he and Amaya beat Fhuere and that Amaya slashed her throat. Long also told the officers where to find the knife that Amaya used, and he stated that Amaya had bitten Fhuere during the assault. A forensic dentist later matched the bite mark to a dental impression of Amaya's teeth. DNA testing established the presence of Fhuere's blood on Amaya's shoe. Amaya wrote letters confessing to the crimes.
Both Long and Amaya were charged with first degree murder. Amaya was also charged with use of a deadly weapon to commit a felony and first degree sexual assault. Long entered into a plea agreement with the State. In exchange for his testimony against Amaya, the charges against Long were reduced to aiding and abetting second degree murder and aiding and abetting first degree sexual assault. Long was sentenced to 25 years' to life imprisonment on the murder conviction and 5 to 10 years' imprisonment on the sexual assault conviction.
Amaya's appointed trial counsel deposed Long after Long had entered into the plea agreement but before Amaya had entered his no contest pleas. The deposition revealed that Long had significant drug, alcohol, and mental health issues that began in his early teens and continued at the time of the deposition. It also revealed that he had given several statements about Fhuere's death to the police and that, in general, each succeeding statement tended to mitigate his culpability and exaggerate Amaya's. Long stated during this deposition that the written statement he had given to police on July 16, 1998, was truthful. He also stated, however, that he was extremely intoxicated the night of the murder and that some of the details in the statement were not correct. He admitted that he had also told officers that evening that he had blacked out and could not remember everything that had happened.
After Long had been deposed, and after being fully advised of his rights, Amaya entered the no contest pleas in exchange for the State's agreement not to seek the death penalty or introduce evidence of aggravating circumstances. Prior to entering the pleas, Amaya wrote a letter to his *26 attorneys expressing his desire to avoid the death penalty. The pleas were entered on October 19, 1999, and Amaya was sentenced on November 19. On November 22, counsel wrote a letter to Amaya informing him of his right to appeal. The letter advised Amaya that the deadline for filing a notice of appeal was December 20, 1999, and further stated:
If you wish to appeal, or discuss that matter further, please notify me as soon as possible so that I will have time to prepare and file the necessary paperwork. Since some of the appeal documents require your signature, I have enclosed with this letter the following:
1. Application to Proceed In Forma Pauperis;
2. Financial Affidavit;
3. Motion and Order.
If you decide to appeal, you must complete these pleadings, sign them, have your signature notarized and return them to my office no later than December 20, 1999.
On December 9, 1999, counsel received a letter from Amaya stating in part: "Here are the forms you sent me all filled out. About the appeal they could reduce my time but they could not give me more or more charges right? Please get a hold of me to let me know." Counsel replied on the same day and advised Amaya of the State's statutory right to appeal a sentence as excessively lenient. Counsel further stated in the same letter that he did not recommend filing an appeal, but that the final decision on the matter was Amaya's. The letter specifically stated: "If you do wish to appeal, please let me know and the appeal will be filed. The appeal must be on file on or before December 20, 1999." Counsel testified that he received no further direction from Amaya regarding an appeal.
On November 21, 2006, Amaya filed a verified motion for postconviction relief. The motion alleged that he received ineffective assistance of counsel in 10 particulars. After an evidentiary hearing, the district court denied relief in a detailed order analyzing each of Amaya's postconviction claims. Amaya filed this timely appeal.

ASSIGNMENTS OF ERROR
Amaya assigns that the district court erred in (1) denying relief on the 10 areas of alleged ineffective assistance of counsel set forth in his motion for postconviction relief, (2) failing to determine that trial counsel did not conduct proper discovery with regard to Long's statements, and (3) failing to determine that trial counsel did not file a direct appeal after being asked to do so.

STANDARD OF REVIEW
[1] On appeal from a proceeding for postconviction relief, the trial court's findings of fact will be upheld unless such findings are clearly erroneous.[1]

ANALYSIS
[2,3] Amaya's first assignment of error is very broad and is not argued in his brief. An alleged error must be both specifically assigned and specifically argued in the brief of the party asserting the error to be considered by an appellate court.[2] Accordingly, we address only the two assignments of error which Amaya has argued.


*27 INVESTIGATION OF LONG'S STATEMENT PRIOR TO PLEAS
[4,5] As noted, Amaya entered pleas of no contest to the charges on which he was convicted. A plea of no contest is equivalent to a plea of guilty.[3] Normally, a voluntary guilty plea waives all defenses to a criminal charge. However, in a postconviction proceeding brought by a defendant convicted because of a guilty plea or a plea of no contest, a court will consider an allegation that the plea was the result of ineffective assistance of counsel.[4] In his motion for postconviction relief, Amaya alleged that his trial counsel was ineffective in failing to "[a]dequately pursue discovery" in order to obtain information regarding Long's "`[d]eal'" with the prosecutor.
[6-8] Familiar principles of law govern our consideration of this claim. In order to establish a right to postconviction relief based on a claim of ineffective assistance of counsel, the defendant has the burden first to show that counsel's performance was deficient; that is, counsel's performance did not equal that of a lawyer with ordinary training and skill in criminal law in the area.[5] Next, the defendant must show that counsel's deficient performance prejudiced the defense in his or her case.[6] The two prongs of this test, deficient performance and prejudice, may be addressed in either order.[7] When a conviction is based upon a guilty plea or a plea of no contest, the prejudice requirement for an ineffective assistance of counsel claim is satisfied if the defendant shows a reasonable probability that but for the errors of counsel, the defendant would have insisted on going to trial rather than pleading guilty.[8]
To buttress his argument that his trial counsel failed to conduct sufficient "discovery" with respect to Long, Amaya directs us to an affidavit executed by Long in 2007, after Amaya filed his postconviction motion. In this affidavit, Long avers that in his July 16, 1998, statement to police, he falsely placed the blame on Amaya in order to exact revenge after police told him that Amaya had implicated him in the crimes. Long further stated in the 2007 affidavit that he did not "know for sure what went on the night of the crime" because he was so "high and drunk" that he could not "remember what I was doing let alone what ... Amaya was doing." Amaya argues that Long's statement to police was the key piece of evidence against him and that if his counsel had done more to investigate, Long's statement would have been discredited before he entered his pleas. Without expressly saying so, Amaya implies that if Long's statement had been properly tested by his counsel, he would not have agreed to enter his pleas.
[9] The record clearly reflects that Amaya's trial counsel did not accept Long's July 16, 1998, statement at face value. Before Amaya entered his pleas, counsel deposed Long with respect to the various statements Long had given to police. This questioning established that Long had at times lied to police, but he *28 maintained that his written statement implicating Amaya in the crimes was true. Also, Long's plea agreement with the prosecutor was produced at his deposition.
In a deposition received at the postconviction hearing, Amaya's trial counsel testified that Long's anticipated trial testimony was only a part of the body of incriminating evidence confronting Amaya at the time he entered his no contest pleas. Other items included the victim's blood on Amaya's shoe, the determination of a forensic dentist that Amaya had inflicted the bite wound, and various letters in which Amaya had confessed to the crimes. The district court agreed with trial counsel's characterization of this evidence of guilt as "bordering on overwhelming." The district court also determined that Amaya's allegations that trial counsel did not adequately investigate Long's statements were "patently frivolous." The court further determined that Long's 2007 affidavit had "no credibility whatsoever," because it was "impossible to separate fact from fiction in anything which Long says about this case or Amaya's involvement therein." Based upon our review of the record, the district court's findings of fact on this issue are not clearly erroneous, and therefore, we conclude that the court did not err in denying this claim for postconviction relief.

ALLEGED FAILURE TO FILE DIRECT APPEAL
[10, 11] Amaya contends that his trial counsel was ineffective for failing to file a direct appeal in response to his request that he do so. Under certain circumstances, the nature of counsel's deficient conduct in the context of the prior proceedings can lead to a presumption of prejudice, negating the defendant's need to offer evidence of actual prejudice in a post-conviction case.[9] After a trial, conviction, and sentencing, if counsel deficiently fails to file or perfect an appeal after being so directed by the criminal defendant, prejudice will be presumed and counsel will be deemed ineffective, thus entitling the defendant to postconviction relief.[10]
[12] Assuming without deciding that the same principle would apply where conviction is the result of a guilty or no contest plea, the critical question of fact is whether Amaya directed his counsel to file a direct appeal on his behalf. After reviewing the evidence received at the postconviction hearing, the district court concluded that he did not. As noted above, the final letter which counsel sent to Amaya specifically requested that Amaya notify him if he wished to file an appeal. After receiving conflicting evidence, the district court found that counsel "never heard again" from Amaya and that Amaya's statements to the contrary were not credible. Based upon our review of the record, we conclude these findings are not clearly erroneous.

CONCLUSION
For the reasons discussed, we conclude that the district court did not err in denying Amaya's motion for postconviction relief, and we affirm its judgment.
AFFIRMED.
NOTES
[1]  State v. Barnes, 272 Neb. 749, 724 N.W.2d 807 (2006); State v. Ortiz, 266 Neb. 959, 670 N.W.2d 788 (2003).
[2]  State v. Dockery, 273 Neb. 330, 729 N.W.2d 320 (2007); State v. Kuehn, 273 Neb. 219, 728 N.W.2d 589 (2007).
[3]  State v. Lassek, 272 Neb. 523, 723 N.W.2d 320 (2006); State v. Gonzalez-Faguaga, 266 Neb. 72, 662 N.W.2d 581 (2003).
[4]  State v. McLeod, 274 Neb. 566, 741 N.W.2d 664 (2007).
[5]  State v. Bazer, 276 Neb. 7, 751 N.W.2d 619 (2008); State v. Smith, 269 Neb. 773, 696 N.W.2d 871 (2005).
[6]  Id.
[7]  State v. Lopez, 274 Neb. 756, 743 N.W.2d 351 (2008).
[8]  State v. McLeod, supra note 4.
[9]  State v. Davlin, 265 Neb. 386, 658 N.W.2d 1 (2003); State v. Trotter, 259 Neb. 212, 609 N.W.2d 33 (2000).
[10]  State v. Barnes, supra note 1; State v. Deckard, 272 Neb. 410, 722 N.W.2d 55 (2006).
