Following a jury-waived trial in the Superior Court, a judge rendered a judgment in favor of the plaintiff, Quality Assured Software, Inc. (QAS), on its breach of contract claim. On appeal, the defendant, Tracelink, Inc. (Tracelink), claims that the judge erred by refusing to issue written findings of fact and rulings of law pursuant to Mass.R.Civ.P. 52(a), as amended, 423 Mass. 1402 (1996). We affirm.

Background. In 2011, QAS and Tracelink entered into a placement agreement (contract) whereby QAS introduced candidates to fill certain positions at Tracelink. In December, 2013, QAS submitted the resume of Michael Owings to Tracelink. In October, 2014, Tracelink offered Owings a position, and Owings started work at Tracelink in January, 2015. Upon learning of Tracelink's hiring of Owings, QAS demanded payment of its fee under the contract. Tracelink refused to pay, contending that the hiring of Owings was primarily due to the personal recommendation of its vice president, Mike Davies (who had previously worked with Owings), and because "so many months had elapsed since [QAS] had forwarded Owings'[s] resume to [Tracelink]." Hence, QAS filed a complaint in the Superior Court alleging, inter alia, breach of contract.

Immediately before trial, the parties notified the judge that they were seeking a jury-waived trial. The judge advised that because he had not been properly notified of the jury waiver (and thus the parties had not complied with the judge's pretrial order for jury-waived cases), the parties could choose any of three options: (1) proceed immediately by way of jury trial; (2) comply with the standard pretrial order "in an expedited fashion," try the case, and wait for written findings and rulings; or (3) proceed immediately to a jury-waived trial, waive the Mass.R.Civ.P. 52(a) requirement to make findings of fact and rulings of law, and receive an immediate verdict. The parties chose the third alternative, and executed a written waiver memorializing the agreement to waive written findings of fact and rulings of law required by rule 52(a).2

On the first day of trial, the parties completed the presentation of witness testimony and evidence. On the second day of trial, immediately prior to closing arguments, Tracelink filed a request for written findings of fact and conclusions of law. The judge, reiterating that the parties had agreed to the procedures utilized at trial, asked Tracelink to explain the change in position. Tracelink's counsel responded, inter alia, that he had concerns with the simplistic nature of the verdict slip, and that the verdict slip should address whether the lapse of time before the hiring of Owings was "reasonable" such that the fee to QAS was still viable. The judge granted the parties time to amend the verdict slip to address Tracelink's concerns. Following a brief recess, the parties submitted a revised verdict slip, which contained two additional questions.3

Following closing argument, the judge made verbal findings on the record regarding the credibility of witnesses, answered each question on the revised verdict slip, rendered a verdict for QAS in the amount of $39,000, and explained the reasons for the verdict. Tracelink filed a posttrial motion for written findings of fact and rulings of law or a new trial, which the judge denied in a written order and memorandum.4 Tracelink then filed a motion for reconsideration and recusal of the judge, which the judge likewise denied in a written order and memorandum. This appeal ensued.5

Discussion. Tracelink contends that the judge erred in refusing to issue written findings of fact and rulings of law as required by the plain language of Mass.R.Civ.P. 52(a).6 We disagree. Tracelink's argument and brief inexplicably neglect to mention that the parties explicitly stipulated, on the record and in writing, to waive rule 52(a) findings and proceed via submission of an agreed upon verdict slip containing special questions. The judge had described the proposed procedure at length, and the parties unequivocally consented thereto. We are unaware of any legal authority, and Tracelink cites to none, supporting the proposition that a party may not waive the application of rule 52(a). To the contrary, even constitutional rights in criminal cases may be waived by a defendant, so long as such waivers are given knowingly and voluntarily. See, e.g., Ciummei v. Commonwealth, 378 Mass. 504, 507 (1979).7

Tracelink does not contend that the waiver was unknowing or involuntary. Further, Tracelink does not argue that the judge abused his discretion in refusing to vacate the stipulation. See Loring v. Mercier, 318 Mass. 599, 601 (1945) (explaining that a court "may vacate a stipulation made by the parties if it is deemed improvident or not conducive to justice"); Kalika v. Munro, 323 Mass. 542, 543 (1948) (noting that "a party may not disregard a stipulation given by him, nor can he revoke or escape from it at his will. His consent, once made a part of the record, binds him until he is relieved from it by judicial action"). Instead, Tracelink argues, without providing context and without acknowledging the posture in which the issue arose in the trial court, that the judge erred in refusing to comply with the mandatory language of rule 52(a). This conclusory argument, unsupported by any legal authority, does not constitute appellate argument within the comprehension of Mass.R.A.P. 16(a)(4), as amended, 367 Mass. 921 (1975), and thus we do not consider it. See Morris v. UNUM Life Ins. Co. ofAmerica, 66 Mass. App. Ct. 716, 723 (2006).

Tracelink also posits that "the judge was predisposed to a ruling for [QAS]" because the judge inquired about settlement during a sidebar conversation. Tracelink contends that the judge's bias was evident because "[t]he only witness to have testified at th[at] point was [QAS's president]. Not a single [d]efense witness had yet taken the stand and the judge was already intimating that he was leaning toward a finding for [QAS]." Thus, Tracelink maintains, written findings were necessary. Contrary to this argument, the chief executive officer of Tracelink had already testified prior to the judge's comment regarding possible settlement. Indeed, he was the first witness called in the case by QAS, and he was cross-examined by Tracelink's counsel.8 Accordingly, Tracelink's claim that the judge erroneously formed an opinion "before any of the [d]efense witnesses had taken the stand" is misleading.9 We further note that Tracelink did not appeal from the denial of its motion for reconsideration and for recusal, see note 4, supra, and thus the issue of the judge's alleged bias was not properly preserved for appellate review. See Mass.R.A.P. 16(a)(4).10 Accordingly, we deny Tracelink's request to remand the case for a new trial.11

Judgment affirmed.