HAYNSWORTH, Senior Circuit Judge:

In a petition for a writ of habeas corpus in the District Court for the District of Rhode Island, Souza contends that the refusal to disclose the identity of a confidential informant and the giving of two supplemental jury instructions denied him a fair trial in the state court. The district judge denied the writ, and we affirm.

At approximately 10 o’clock in the evening, two masked men, armed with handguns, entered a liquor store in Pawtucket. They seized the contents of the cash register, robbed the people in the store, and pistol-whipped some of them.

Two policemen arrived on the scene while the robbery was still in progress. There was an exchange of gunfire, and one policeman was seriously wounded. The robbers then attempted to flee. One of them, later identified as David Cochrane, attempted to hide behind a nearby car and was soon captured. The other, however, continued running and was pursued by a third policeman who had arrived as a reinforcement. As the robber was scaling a railroad embankment, the policeman fired his pistol and appeared to have hit him. The robber kept going, however, and the policeman lost sight of him in the darkness.

Later the policemen found a trail of blood originating at the place on the embankment where the fleeing robber appeared to have been hit. The trail ended almost a mile away, outside a house in which Souza’s aunt lived. 1

Robert DePaulo testified that, earlier in the evening of the robbery, Souza and Cochrane had visited him and his girlfriend in her apartment. They sought to borrow some personal articles. According to De-Paulo, sometime after 11 o’clock that night Souza returned to the apartment with a bleeding wound in his left arm. DePaulo dressed Souza’s wound and provided him with a fresh set of clothing. Souza told him of the robbery, but not of the shooting of the policeman. DePaulo undertook to burn Souza’s soiled clothes and to hide his gun. He telephoned Souza’s girlfriend and had her pick him up.

Some hours later, DePaulo telephoned the Pawtucket police and informed them of the matter. He was prompted to do that, he said, when he learned that a policeman had been seriously wounded.

DePaulo’s girlfriend corroborated his testimony.

During pretrial discovery, Souza’s lawyer learned of an affidavit in support of an application for a tap on the telephone used by DePaulo. The affiant stated that he had been informed by a confidential informant that DePaulo had been involved in the robbery as the driver of the getaway car. Souza’s lawyer sought disclosure of the identity of that informant.

II.

Souza first complains of the trial court’s refusal to disclose the identity of the confidential informant. The contention was presented to the Supreme Court of Rhode Island and denied in an elaborate opinion. State v. Souza, 425 A.2d 893 (R.I.1981). It balanced the state’s interest in maintaining the anonymity of a confidential informant against the defendant’s interest in obtaining the testimony of that informant. In this case, the informant’s testimony could have been used for impeachment purposes, showing DePaulo’s direct involvement in *1531 the enterprise. The marginal value to the defendant of this impeachment evidence is questionable, however, because in his testimony DePaulo admitted complicity in harboring Souza and in undertaking to dispose of the gun and of the clothing which might have been useful as evidence against Souza. Furthermore, a police official testified that DePaulo had been a suspect in the case.

In the district court, extensive consideration was given to this contention. The analysis of the district judge began with Roviaro v. United States, 353 U.S. 53, 77 S.Ct. 623,1 L.Ed.2d 639 (1957), and proceeded to a consideration of other relevant cases. The district court recognized that the state must disclose the identity of the informer if such disclosure would be relevant and helpful to the defense of the accused. After carefully analyzing Souza’s need for the informant’s testimony, however, the district judge concluded that, in light of all of the circumstances, any benefit to the defense from the testimony would have been speculative and that its admission would not likely have affected the outcome of the trial.

After considering the potential relevance and helpfulness of the informant’s testimony, the district court inserted a footnote stating that the Supreme Court of Rhode Island had made a specific finding that its admission would not have affected the jury’s verdict. The district court concluded that this finding was due deference under the rule of Sumner v. Mata, 449 U.S. 539, 101 S.Ct. 764, 66 L.Ed.2d 722 (1981).

One need not wonder that the district judge labelled this finding, that there was no reasonable likelihood the testimony of the informer would have affected the outcome, as one of fact. It resembles a finding of fact. It is not, however, a conclusion based directly upon evidence. Instead, it is derived from a process of considering and balancing subsidiary facts and circumstances. In a state prisoner’s habeas corpus case, a reviewing court may be required to accept findings of subsidiary facts unless one of the exceptions to 28 U.S.C.A. § 2254(d) is present. 2 The balancing process itself, however, remains subject to plenary review. This would seem plain if the balancing process had followed the form outlined in Roviaro. Although that process may be distilled into a search for the answer to a single question, whether there is a reasonable likelihood of an effect upon the outcome, the search for that answer still involves the process of considering and balancing the subsidiary facts.

This ultimate conclusion is subject to plenary review as one of law. Napue v. People of State of Illinois, 360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959); Hamric v. Bailey, 386 F.2d 390 (4th Cir.1967). This court has granted such plenary review of the same question in a state prisoner’s habeas corpus case. Zeigler v. Callahan, 659 F.2d 254 (1st Cir.1981). The district court was thus mistaken in stating in its footnote 4 that deference was due to the state court’s ultimate conclusion that the informant’s testimony would have carried with it no reasonable likelihood of an effect upon the outcome.

The presence of this footnote, however, does not require reversal, for the district court had already given extensive consideration to the controlling legal principle as applied to the relevant subsidiary facts in this case. His conclusion cannot be faulted because, as a seeming after-thought at the end of his discussion of the matter, he inserted a footnote with an erroneous reference to the doctrine of Sumner v. Mata.

111.

The jury’s deliberations began on a Friday. They continued for a full day on Saturday, and the jury returned at noon on Sunday. At that time, the trial judge gave them a mild version of the Allen charge (see Allen v. United States, 164 U.S. 492, 17 S.Ct. 154, 41 L.Ed. 528 (1896)), but then *1532 informed the jurors that if they were genuinely divided on issues which prevented their return of a verdict by 4 o’clock that afternoon, he would “accept from” the jury that they were hopelessly deadlocked and discharge them. The verdict of guilt was returned before the 4 o’clock deadline.

It is contended that setting the deadline was coercive and an unconstitutional deprivation of Souza’s right to a fair trial. We cannot agree.

In some circumstances, setting deadlines for jury agreement may be coercive and a serious impairment of a defendant’s right to a fair trial. See Goff v. United States, 446 F.2d 623, 626 (10th Cir.1971); United States v. Lansdown, 460 F.2d 164, 169 n. 3 (4th Cir.1972). There can be no per se rule, however, for the effect upon a jury of the fixing of a deadline varies greatly with the circumstances. In this case, the judge, in his preceding breath, told the jurors not to abandon conscientiously held beliefs or firmly held convictions. The deadline was to be operative only if at 4 o’clock the jury was “genuinely divided” on issues which would prevent the return of a verdict. The jurors must have understood that if at 4 o’clock they were close to agreement they would be allowed such additional time as they might need. It was only if they reported at 4 o’clock that they could not agree that they were to be discharged.

Under these circumstances, fixing the 4 o’clock deadline seems the antithesis of coercion. Jurors on either side of any disagreement were relieved of the possible dread that they might be kept until late in the afternoon and brought back again on Monday morning to resume their deliberations. The fixing of the deadline tended to reinforce the admonition that firmly held views were not to be surrendered rather than to counter it.

IV.

At one point in his supplemental instructions, the trial judge informed the jury that a reasonable doubt “is an actual and substantial doubt.” It was an isolated statement in full instructions which otherwise quite correctly defined reasonable doubt and explicitly informed the jurors that a verdict might not be found upon suspicion, however strong that suspicion might be.

Any error in this supplemental charge was not of constitutional dimension. Souza was fairly tried and fairly convicted.

The district court properly concluded that there was no constitutional infirmity in the state court proceedings.

AFFIRMED.

. A specimen from the trail of blood was found to be Type A. A subsequent test revealed that the petitioner has Type A blood.

. Similarly, while a finding of fact made by a federal district court must be affirmed unless it is shown to be clearly erroneous, that standard does not apply to the review of an ultimate conclusion such as this.