Christopher Stacy Pool appeals the denial of his petition for habeas corpus. His case has been ably argued on appeal, but we affirm the decision of the district court.

FACTS AND PROCEEDINGS

In 1982 Pool was a thirty-year-old produce salesman. He was out on bail pending trial for assault. He had been convicted in 1977 of possessing marijuana and had served a three year sentence of probation.

On the evening of February 19, 1982, Pool was driving his father’s Toyota in a deserted part of Yuma County, accompanied by his friend Brian Twist. Twist had invited Pool to go rabbit-hunting and Pool had brought a gun with him; but Twist suggested that Pool first aid him in planting two marijuana plants and as they drove they looked for a place to plant the plants.

Paul Connolly, a deputy sheriff of Yuma County, was working that night for a private employer, Camille Allec, patrolling for pay to catch thieves in Allec’s citrus groves. Connolly had worked in this capacity for two years and had made about thirty stops or arrests. He drove a “beat up” Yuma County Sheriff Department’s 1969 Ford pickup truck, not readily identifiable as a police vehicle. He himself was wearing levis, boots, and his uniform shirt with gold letters and gold circles on the arms and his police badge and name plate; he was also wearing a gun and gunbelt.

Connolly passed Pool in the Toyota and made a U-turn to follow him, eventually finding the Toyota parked on a rural road. Connolly parked head-on with the Toyota. There was no street lighting. Connolly’s own lights lit up the car, and he saw two people in the front seat and the plants in the rear. Connolly radioed his number, his location, the license number of the Toyota and the fact that it had marijuana in it to the Sheriff’s Department. He then turned on the red grill lights of his truck, walked in front of these lights and approached the driver’s side of the Toyota.

According to his testimony at the trial, Connolly had his flashlight in his right hand and shined the light into the truck. He saw the driver reach for his midsection and noticed a bulge on his right side. He ordered both driver and passenger to put their hands on the dashboard. He heard the driver say “fucking pig.” He saw the top two inches of an automatic pistol. With his right hand — his shooting hand— occupied with the flashlight, Connolly believes he threw the light into the car. He yelled and dove into the bushes, down a bank. As he dove, or just before, he heard the pop of a shot. He rolled twice, then turned, and fired back twice at headlights that turned out to be his own. One bullet was later found to have damaged the truck’s radiator, the other to have ricocheted off, leaving a dent. After his two shots, he crawled into a small hole. About 20 minutes later, Deputy Will Brooks drove up. The Toyota had gone. Connolly came out of the hole and told Brooks that “two Indians just took a shot at me and are armed with a .45 or .9 mm.”

At the trial, Pool and Twist testified that they were blinded by Connolly’s lights. *779 When Connolly told them to place their hands on the dashboard, Pool was scared and reached for the gun. As he pulled up the gun he was hit in the face with the flashlight. To this extent, Pool and Twist’s testimony was not contrary to Connolly’s. Pool, however, denied saying anything to Connolly except “Get back” as he, Pool, put his hands on his gun, and both Pool and Twist maintained that they did not recognize Connolly as a police officer. On the critical issue of the shooting, Pool testified that before he fired he heard “a cannon blast” in his car and thought, “This man is trying to kill me.” He then “cocked the gun and stuck it out the window and fired a shot at the same time trying to start the car.” As he drove off, Pool heard “at least two shots.” Twist’s testimony as to the events was vague and not such as to inspire confidence in his memory or veracity. In his own words, he was “in total confusion.”

Pool was charged with the crime of aggravated assault with a deadly weapon. His defense was that he acted with justification. His first trial ended in a hung jury. In the second trial, the judge charged the jury that Pool was justified if two conditions were satisfied: that a reasonable person in his situation would have believed that physical force was immediately necessary to protect against another’s use or attempted use of unlawful physical force; and that he used or threatened no more physical force than would have appeared necessary to a reasonable person in his situation. No objection was made to this standard instruction. The case was sent to the jury at 6:12 p.m. and at 7:26 p.m. the jury returned a verdict of guilty.

Douglas W. Keddie, the trial judge, denied a motion for a new trial on July 13, 1982. He sentenced Pool to nine years in prison. Pool appealed to the Arizona Court of Appeals, attacking the admission of the marijuana and evidence of his bail status. He also challenged a limitation put on the cross-examination of Connolly and Brooks and the exclusion of expert testimony on proper procedures for a police stop. Other errors assigned were the denial of a directed verdict; denial of a motion to change the judge who was accused by Pool of prejudice; error in the jury instruction on Pool’s bail status; and error in rejecting Pool’s proffered instructions on retreat. The Court of Appeals affirmed the conviction; the Supreme Court of Arizona refused to review.

Pool, represented by new counsel, applied for habeas corpus. A magistrate recommended that his petition be dismissed without an evidentiary hearing. The district court accepted this recommendation and on March 10, 1986 denied the petition. Pool appealed to this court.

ISSUES

Pool presses two claims:

First, Pool maintains he was denied his rights under the Sixth Amendment “to present a defense.” Washington v. Texas, 388 U.S. 14, 19 , 87 S.Ct. 1920, 1923 , 18 L.Ed.2d 1019 (1967). He sought to put on the stand a detective from the City of Yuma Police Department who as an expert would testify as to the proper police procedure to be used by an undercover officer identifying himself. The detective had testified at the first trial which ended in a deadlocked jury; Judge Keddie, who presided at both trials, stated that by the time of the second trial he had been persuaded by the prosecutor’s objections that the testimony was irrelevant and that the jury did not need it to understand the situation. Pool contends that the detective’s testimony “directly rebutted the theory of the government’s case that a reasonable person would have identified Mr. Connolly as a police officer.”

Second, Pool points to matter that Judge Keddie’s rulings precluded both juries from hearing: Five days after the encounter with Pool, Connolly was reprimanded for not reporting that he had been working for two years for pay for a private employer and using the county’s truck and gas; also for not giving “an adequate answer” to the Sheriff’s inquiry as to why the Sheriff had not been informed. Connolly was docked “100 hours of comp time” to compensate for the gas and wear and tear on the truck. *780 The reprimand was to stay in his file one year.

The reprimand became an issue when defense counsel wanted to show that Connolly had lied to defense counsel in his pretrial statements. As part of that proof, defense counsel sought to introduce the reprimand. Judge Keddie interpreted the pretrial statements made by Connolly to defense counsel as ambiguous and did not believe the reprimand relevant to Connolly’s credibility. Accordingly, he refused to allow examination on either the reprimand or the statements to counsel.

On appeal to this court, Pool urges that cross-examination on the reprimand was necessary to bring out bias against Pool on Connolly’s part. As expressed by Pool’s brief:

Pool argues further that Connolly’s reprimand could be interpreted as a reprimand for equivocating when questioned by the Sheriff and in this way would also have a bearing on his credibility. Denial of the opportunity to attack Connolly's credibility is, Pool maintains, a violation of the right “to be confronted with witnesses against him.” United States Constitution, Amendment VI; Davis v. Alaska, 415 U.S. 308 , 94 S.Ct. 1105 , 39 L.Ed.2d 347 (1974).

ANALYSIS

We review anew the legal issues presented to the district court. Chatman v. Marquez, 754 F.2d 1531 (9th Cir.1985).

First. The admissibility of expert testimony is normally in Arizona as elsewhere a matter of discretion for the trial judge. State v. Williams, 132 Ariz. 153, 160 , 644 P.2d 889 (1982). Expert testimony is unnecessary if the jury is qualified without such testimony to determine the issue intelligently. State v. Chapple, 135 Ariz. 281, 292-93 , 660 P.2d 1208 (1983). We do not find Arizona’s application of these standard doctrines to have violated the Sixth Amendment. If the jury believed Connolly, the jury would have found that Pool knew he was police because he used the opprobrious street term for a policeman. If the jury believed Pool himself, the jury would have found that Pool fired after being shot at by Connolly. Without expert testimony the jury would have known that such an approach by Connolly would not constitute proper police procedure. If the jury did not believe Pool, the expert’s testimony would not have helped him. No constitutional error was committed in excluding the testimony. In any event, the expert testimony would have been cumulative and was not “a major part of the attempted defense.” Perry v. Rushen, 713 F.2d 1447, 1453 (9th Cir.1983).

Second, as to the reprimand: the observation in it that Connolly’s answer was “inadequate” does not show that he was a liar; the observation merely means that he did not have a good explanation. That the Sheriff’s Department already had a good idea of Connolly’s practice is evident from the arrests he had made in the past and the police communications he used; it is a reasonable inference that the reprimand came about because of the publicity. In ruling on peripheral evidence, a trial court must have a range of discretion within which a mistake, if there is one, is not automatically constitutional error. Police discipline of a police witness may be the only evidence of possible bias and so severe in degree that a motive to lie may be created. Cf. United States v. Garrett, 542 F.2d 23 (6th Cir.1976). In Pool’s case, the existence of the reprimand in Connolly’s file would not have significantly increased his desire to ingratiate himself with his superiors. He had already lost “the comp time.” The reprimand was to be removed from the file within nine months of the trial. Every police officer, it may be supposed, looks better with a certain kind of superior if his testimony leads to a conviction. This possible reason for discounting police testimony is not materially enhanced *781 by the presence of a mild, soon-to-be extinguished censure. Finally, that the encounter with Connolly had led to the reprimand would not have shown that Connolly had a different degree of bias against Pool than the jury already knew that he had. The jury knew from Connolly’s own lips that Pool had put him to flight, driven him into a hole, and led him to shoot up his own vehicle. If the jury did not infer from this story that Connolly could have little love for the defendant, a bureaucratic censure would not have changed the jury’s view of Connolly’s animus. No constitutional right was denied in limiting the cross-examination in this regard. Unlike Davis v. Alaska where a traditional method of impeaching a witness was denied by the trial court, there was here only a remote and peripheral challenge to Connolly’s credibility.

AFFIRMED.