POLITZ, Circuit Judge:
Ramon G. Garza and Alfredo R. Menchaca challenge their convictions by a jury of violations of 18 U.S.C. §§ 241 and 242, and as to Garza, 18 U.S.C. § 1503, claiming that the trial court erred in making certain evidentiary rulings, in giving its jury charge and in declining to collaterally estop parts of the prosecution. They further contend that the verdicts are not supported by sufficient evidence. As discussed infra, we find merit in some challenges but are persuaded that the trial errors did not result in an unfair or constitutionally infirm trial and, because of the overwhelming evidence of guilt, are appropriately categorized as harmless error. Accordingly, we affirm.
Facts and Procedural Background
Shortly after assuming office as sheriff of Zavala County, Texas, Garza hired Menchaca as a special investigator. Menchaca could not be commissioned as a deputy sheriff because a prior conviction prevented him from being certified for that job. Two and a half years after Garza became sheriff he and Menchaca were named in a 15-count indictment charging violations of 18 U.S.C. §§ 241, 242, 1512 and 1584. They were charged with conspiracy and substantive counts involving the denial of the civil rights of persons arrested and confined in the Zavala County jail. The indictment charged that appellants arrested persons without warrants and without probable cause, detained them for long periods, subjected them to repeated questioning, and failed to take them before a magistrate as required by Texas law. Appellants were also charged with one count of holding a person in involuntary servitude. Additionally, Menchaca was charged with obstruction of justice for trying to prevent a co-employee from informing the FBI about federal violations by appellants.
After an eight-day trial the jury convicted appellants of one substantive § 242 count for holding a prisoner for 36 hours in an isolation cell measuring 32" by 49", without lights, water, bedding or toilet.1 Appellants were acquitted of seven substantive § 242 counts, the involuntary servitude count and the obstruction of justice charge. The jury could not reach a verdict on the conspiracy count and on four of the § 242 counts and a mistrial resulted.
Following the mistrial, the grand jury returned a six-count indictment charging the § 241 conspiracy and the four § 242 counts on which the jury had hung and, in addition, charging Garza with a violation of 18 U.S.C. § 1503 for firing a deputy sheriff who had testified as a government witness at the first trial. Appellants were jointly tried on the first five counts and the jury returned verdicts of guilty on all charges. In a separate trial a few days later Garza was found guilty of the remaining § 1503 count. This appeal follows.
I. Evidentiary Rulings
A. Prior convictions
Appellants maintain that the trial judge committed reversible error when he allowed the prosecution to introduce evidence of Menchaca’s prior felony convictions, one for the illegal importation of meat in 1952 and one for the illegal importation of marihuana in 1954.2 This issue was addressed [1205]*1205by the court both before and during the trial.
By an in limine motion, appellants sought to prevent use of this evidence. At a pretrial hearing shortly before trial the court questioned the admissibility of the evidence but stated that the subject matter would be appropriate in the cross-examination of any character witnesses Menchaca might offer. The prosecutor argued that the evidence was relevant to prove intent, offering this syllogism. Menchaca’s felony conviction prevented his certification as a peace officer. Only one so certified could validly arrest under Texas law. Menchaca violated Texas law when he made arrests so Menchaca intended to deprive those arrested of their civil rights. The court deferred ruling until the morning of trial. Prior to selecting the jury the court disposed of all pending motions, including that involving Menchaca’s prior offenses. No definitive ruling resulted, the court merely repeated its prior inclinations and deferred ruling until necessary at trial.
The issue next arose during the testimony of Alfred Villarreal, general counsel for the Texas Commission on Law Enforcement Standards and Education. Over objection of defendants Villarreal testified that Menchaca was not qualified to be a certified police officer because “Mr. Menchaca maintains a prior felony conviction.” The court immediately admonished the jury:
Ladies and gentlemen of the jury, at this time, I will caution you that even though this witness has testified that that is his belief as the basis of disqualification of Mr. Menchaca, until such time as it’s actually connected up, you will just hold that in the back of your mind and not consider it except that there’s been testimony about it. If it is not, in fact, proven up, then the Court will instruct you to disregard it entirely____ I will instruct you now that although you’re aware of the testimony that ... Mr. Villarreal believes that there was, in fact, a felony conviction that would disqualify [Menchaca] from being a qualified peace officer, that until such time as that proof comes in, if it ever comes in, you’re to only hold that in the back of your mind, and I’ll give you instructions concerning how you may use that information.
The prosecutor later attempted to prove the conviction by offering copies of court records. Defendants vigorously objected arguing, inter alia, that the prejudicial effect far outweighed the probative value, citing Fed.R.Evid. 403. Concerned about the fairness of the evidence and the danger that its use might “cloud the issue” and “confuse the jury”, the court ruled: “at this time, I’ll admit them only for the purpose of the record and not allow the Government to introduce them further.” No further effort was made to use the convictions in the evidence.
The final reference to the convictions came in the rebuttal phase of the closing argument when in response to defendants’ attack on several government witnesses because of their prior convictions the prosecutor stated: “But half of the defense case has been testimony of a convicted felon, as well, and that’s Mr. Menchaca.” Counsel objected and the following colloquy ensued:
(AT THE BENCH)
THE COURT: What evidence does the jury have of convictions?
MS. ORTIZ: The testimony of Mr. Villarreal, who testified that was why he was ineligible to be a law enforcement officer.
THE COURT: Was that the extent of it? MS. ORTIZ: Yes, sir.
THE COURT: All right. I’ll overrule the objection.
(IN OPEN COURT)
THE COURT: Ladies and gentlemen of the jury, I’ll overrule the objection.
Villarreal’s reference to the prior convictions was properly cabined by the court but the prosecutor’s remark in closing argument was improper. The convictions were never proven. Not being proven they were not relevant. In United States v. Lemaire, 712 F.2d 944, 946-47 (5th Cir.1983), drawing upon and citing our [1206]*1206en banc decision in United States v. Beechum, 582 F.2d 898 (5th Cir.1978), we held:
Indeed, under Beechum, evidence of an extrinsic offense is relevant to intent only if the act in fact occurred and the defendant in fact committed it. Thus, as the predicate to a determination that the extrinsic act is relevant, the government must offer proof establishing that the defendant committed the act. (citations omitted)
The trial court should have sustained counsel’s objection and recalled for the jury the earlier admonition that it was not to consider that part of the testimony of Villarreal unless the convictions were later proven. The jury should have been instructed that the convictions had not been proven.
B. Hearsay exclusion
Appellants urge reversal of their convictions because the court would not permit Menchaca and other officers to testify about what they were told by way of complaints against those arrested. The evidence was barred as hearsay. This was error. The statements were offered in explanation of the arrests. The evidence was offered to prove what was said to Menehaca and the others, not to prove the truth of what was said. The evidence was offered as the fact of an assertion and not as assertion of a fact and was therefore not hearsay. Fed.R.Evid. 801(a), (c). Smith v. Gonzales, 670 F.2d 522 (5th Cir.1982); Lubbock Feed Lots, Inc. v. Iowa Beef Processors, 630 F.2d 250 (5th Cir.1980).
C. Limitation on cross-examination
Appellants next attack their convictions because the trial court disallowed proof of the arrest records of several government witnesses. The government moved in limine to block proof of the arrest records of six witnesses. At a pretrial hearing, defense counsel argued that the arrest records were admissible for impeachment purposes, to reflect on the witnesses’ motive for testifying against the defendant police officers. The evidence was barred. This was error.
Typically, evidence of an arrest may not be used for impeachment of a witness; only evidence of convictions is permitted. Fed.R.Evid. 609. But the case before us is atypical. Here the defendants are police officers. Several of the witnesses had been arrested, sometimes by Garza’s deputies. Evidence of past arrests, and past involvement with the police in general and defendants in particular, would be pertinent in the jury’s essential determination of credibility. Such evidence would be relevant to the issue of bias, prejudice or ulteri- or motive of the witness. Davis v. Alaska, 415 U.S. 308, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974); Carrillo v. Perkins, 723 F.2d 1165 (5th Cir.1984); Greene v. Wainwright, 634 F.2d 272 (5th Cir.1981). In United States v. Croucher, 532 F.2d 1042, 1045 (5th Cir.1976) we held: “The issue of [the witness’] relationship with both state and federal law enforcement officials, in connection with his participation in this case, was highly relevant to his credibility as a witness for the prosecution.”
While it is within the discretionary authority of the trial court to limit cross-examination, that authority “comes into play only after there has been permitted as a matter of right sufficient cross-examination to satisfy the Sixth Amendment.” United States v. Mayer, 556 F.2d 245, 250 (5th Cir.1977); Carrillo v. Perkins, 723 F.2d 1165 (5th Cir.1984). The trial court . erred in prohibiting this line of questioning on cross-examination.
Harmless Error
Despite these errors, a reversal of appellants’ convictions is not warranted. After a studied examination of the record we are convinced that these errors did not prejudice the defense and, because of the overwhelming evidence of guilt, were harmless. Fahy v. Connecticut, 375 U.S. 85, 84 S.Ct. 229, 11 L.Ed.2d 171 (1963) (evidentiary rulings subject to harmless error rule); United States v. Daughtry, 502 F.2d 1019 (5th Cir.1974) (castigation of another jury’s verdict of not guilty); United States v. Lipscomb, 435 F.2d 795 (5th Cir. [1207]*12071970) (evidentiary rulings); Carrillo v. Perkins, 723 F.2d 1165 (5th Cir.1984) (limitation of cross-examination). To withstand attack the error must be harmless beyond a reasonable doubt. Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967); Carrillo v. Perkins, 723 F.2d 1165 (5th Cir.1984); United States v. Crumley, 565 F.2d 945 (5th Cir.1978). Before an error may be considered harmless beyond a reasonable doubt, the reviewing court must determine that “absent the so-determined unconstitutional effect, the evidence remains not only sufficient to support the verdict but [is] so overwhelming as to establish the guilt of the accused beyond a reasonable doubt.” Harryman v. Estelle, 616 F.2d 870, 876 (5th Cir.1980) (en banc). And as we therein further observed:
As the Court stated in Fahy, “it is necessary to review the facts of the case and the evidence adduced at trial” to determine the effect of the unlawfully admitted evidence “upon the other evidence adduced at trial and upon the conduct of the defense.”
The harmless error prescript provides “an exacting standard that must be uncompromisingly applied.” Id.
The Evidential Fabric
The record abounds with proof of the wrongful acts of Garza and Menchaca. Testimony of several witnesses, supported by documentary evidence, portrayed the civil rights violations repeatedly occurring in the Zavala County Sheriffs office. Booking cards reflect that five of the persons named in the indictment, Eugene Sanchez, Roy Burrell, Miguel Diaz, Humberto Pena and Jesus Rodriguez were arrested and held for “investigation” or on no charge at all. Documentary evidence shows that Rodriguez was arrested by Garza on April 8, 1981 and was held without charge until April 14, 1981 when he was finally taken before a magistrate. Miguel Marti was arrested on October 6, 1982 and not taken before a magistrate until October 18, 1982. No warrants were ever issued for the arrest of these individuals and no circumstances were asserted to justify warrantless arrests. Other persons arrested were never brought before the magistrate whose office adjoined the jail. No indictments were brought against Sanchez, Burrell, Diaz, Pena, Rodriguez or Marti.
A former Zavala County deputy sheriff, Jose Rodriguez, who did most of the office’s paperwork, testified that he and Menchaca arrested Marti and Julio Herrera-Castillo on orders from Garza. There were no warrants, no Miranda warnings were given, but these men were arrested, booked, jailed and questioned. They were not brought before the magistrate. Oscar P. Saucedo, employed by Garza as a jailer, filled out booking cards as a regular duty. He testified that Menchaca directed him to place Garza’s name as the arresting officer on Rodriguez’s card and to charge him with “investigation.” The same was true for others arrested. Saucedo confirmed that the arrests set forth in the indictment were warrantless. Deputy Ramirez, also a jailer, testified to substantially the same facts concerning the arrests of Burrell and Sanchez. The former Chief of Police of Crystal City testified that Diaz and Pena were arrested by city officers and one of Garza’s deputies. Shortly after their arrest a lineup was held but they were not identified and they were released by the city police. Menchaca, present for the lineup, immediately re-arrested Diaz and Pena and took them to the county jail. It is disputed whether Garza accompanied Menchaca to the lineup. Deputy Meister testified that Pena was brought in on Menchaca’s orders, arrested without a warrant, booked, held, and questioned, but was not taken before the magistrate.
Garza acknowledged that some persons were arrested without warrants, charged with “investigation,” booked, jailed, questioned and never taken before a magistrate. He disclaimed responsibility for these errors, assigning the blame to his deputies and jailers. When asked why people were held for long periods of time and were not charged or taken before a magistrate, Garza responded that they were [1208]*1208“waiting for the victim to come and sign a complaint.” Menchaca likewise disclaimed responsibility, asserting that it was the duty of others to secure warrants and to take those arrested before a magistrate without undue delay. Both Garza and Menchaca conceded that there was no such crime as “investigation.”
Garza and Menchaca’s defense was that they were merely doing their jobs and sometimes made mistakes. They maintained that there was probable cause to arrest all of the persons named, that Zavala County had a population of 16,000 and many people passed through their jail and only a very few, including those named in the indictment, were improperly arrested and processed.
Given this evidence, the evidentiary rulings complained of had no meaningful impact on the evidence adduced at trial or on the conduct of the defense. The hearsay exclusion related only to the probable cause dimension of the warrantless arrests. Assuming probable cause existed, the evidence uniformly shows that the arrests were warrantless and that after booking the named prisoners were held several days to several weeks without being charged, brought before a magistrate, and advised of their rights. In the meantime they were repeatedly questioned. The exclusion of the arrest records of some witnesses, though error, was harmless. The testimony of those witnesses was corroborated by the testimony of other, unchallenged witnesses and by documentary evidence. Pretermitting the challenged testimony, the evidence of guilt overwhelms. The allowance of the comment by Villarreal that Menchaca maintained a prior felony conviction, and the remark in rebuttal by the prosecutor that Menchaca was a convicted felon do not undermine our confidence in the jury’s decisions. The errors were harmless beyond a reasonable doubt. Harryman v. Estelle.
II. Collateral Estoppel
Menchaca maintains that the government was collaterally estopped from relitigating six substantive charges of which he was acquitted or mistried in the first trial. Those six charges, reappearing as overt acts in the superseding indictment conspiracy count, are as follows:
1. On April 8,1981, Defendant RAMON G. GARZA arrested Jesus Rodriguez for “theft” without probable cause and without obtaining a warrant for his arrest. Thereafter, from April 8, 1981, until his initial appearance before the magistrate on April 14, 1981, Defendants RAMON G. GARZA and ALFREDO R. MENCHACA held Jesus Rodriguez in the Zavala County Jail and interrogated Jesus Rodriguez about the alleged theft without taking him before said magistrate.
2. From November 24, 1981, until his release on December 1,1981, Defendants RAMON G. GARZA and ALFREDO R. MENCHACA held Juan Salazar-Pena in the Zavala County Jail and interrogated Juan Salazar-Pena about an alleged theft without taking him before a magistrate. No charges were ever filed against Juan Salazar-Pena for the alleged theft.
3. On January 3, 1982, Defendant ALFREDO R. MENCHACA arrested Eugene Sanchez for “burglary” and “hit and run” without probable cause and without obtaining a warrant for this arrest. Thereafter, from January 2, 1982, until his release on January 4, 1982, Defendants RAMON G. GARZA and ALFREDO R. MENCHACA held Eugene Sanchez in the Zavala County Jail and interrogated Eugene Sanchez about the alleged burglary without taking him before a magistrate. No charges were ever filed against Eugene Sanchez for the alleged burglary.
4. On February 13, 1982, Defendants RAMON G. GARZA and ALFREDO R. MENCHACA arrested Roy Burrell for “burglary” without probable cause and without obtaining a warrant for his arrest. Thereafter, from February 13, 1982, until his release on February 15, 1982, Defendants RAMON G. GARZA and ALFREDO R. MENCHACA held Roy Burrell in the Zavala County Jail and interrogated Roy Burrell about the alleged burglary without taking him be[1209]*1209fore a magistrate. No charges were ever filed against Roy Burrell for the alleged burglary.
5. On October 6, 1982, Defendant ALFREDO R. MENCHACA arrested Miguel Marti for “burglary” without probable cause and without obtaining a warrant for his arrest. Thereafter, from October 6, 1982 until his appearance before a magistrate on October 18, 1982, Defendants RAMON G. GARZA and ALFREDO R. MENCHACA held Miguel Marti in the Zavala County Jail and interrogated Miguel Marti about the alleged burglary without taking him before said magistrate. Defendants RAMON G. GARZA and ALFREDO R. MENCHACA then held Miguel Marti in the Zavala County Jail for an additional sixty-six days until his release on December 23, 1982.
6. On October 12, 1982, Defendant ALFREDO R. MENCHACA arrested Julio Herrera-Castillo for “burglary” without probable cause and without obtaining a warrant for his arrest. Thereafter, from October 12, 1982 until his appearance before a magistrate on October 18, 1982, Defendants RAMON G. GARZA and ALFREDO R. MENCHACA held Julio Herrera-Castillo in Zavala County Jail and interrogated Julio Herrera-Castillo about the alleged burglary without taking him before said magistrate. Defendants RAMON G. GARZA and ALFREDO R. MENCHACA then held Julio Herrera-Castillo in the Zavala County Jail for an additional thirty-two days until his release on November 19, 1982.
These allegations correspond to substantive Counts 2,11, 4, 6, 8 and 9, respectively, in the first indictment. Menchaca was acquitted on Counts 2, 4, 6, 8 and 9 and was granted a mistrial on Count 11.
Prior to his second trial, Menchaca moved to strike the allegations contained in Overt Acts 1 through 7. He claimed collateral estoppel. The district court held that the jury could have acquitted for more than one reason and therefore litigation involving these incidents was not barred.
The doctrine of collateral estoppel bars relitigation of any issue that has been determined in a prior final and valid judgment. Ashe v. Swenson, 397 U.S. 436, 90 S.Ct. 1189, 25 L.Ed.2d 469 (1970); United States v. Lee, 622 F.2d 787 (5th Cir.1980). When collateral estoppel is asserted by an accused we must determine what facts “were necessarily determined” in the first case and whether the government has tried to “relitigate facts necessarily established against it in the first trial.” United States v. Mock, 604 F.2d 341, 343 (5th Cir.1979); United States v. Lee. By returning a general verdict of not guilty on five counts and by stating it was unable to reach a verdict on the sixth, the jury did no more than announce that it was not convinced beyond a reasonable doubt of at least one essential element of a § 242 offense. The jury may have found wanting the element of specific intent to deprive the individuals of their civil rights. For whatever reason, the jury concluded that proof was lacking that a crime was committed. That finding does not terminate the inquiry before us because overt acts alleged in support of a conspiracy charge need not be crimes. “It is not necessary that the overt act be illegal.” United States v. Khamis, 674 F.2d 390, 393 (5th Cir.1982). “An act innocent in nature and of no danger to society can suffice if it furthers the criminal venture.” United States v. Jones, 642 F.2d 909, 914 (5th Cir.1981), citing United States v. Willis, 583 F.2d 203, 207 (5th Cir.1978). Conspiracy to commit an offense and commission of a substantive offense are separate and distinct crimes. United States v. Khamis; United States v. Garcia, 655 F.2d 59 (5th Cir.1981). “Under the conspiracy charge the government is only required to prove that at least one overt act was taken by one of the conspirators in furtherance of the conspiracy; it need not prove that the substantive offense was consummated.” United States v. Todd, 735 F.2d 146, 151-52 (5th Cir.1984). Merely because appellants were acquitted of the substantive § 242 charges does not mean that the facts upon which the charges were based cannot later be used as [1210]*1210non-criminal overt acts in furtherance of the conspiracy to commit the substantive offenses. Ashe v. Swenson; United States v. Gonzalez, 548 F.2d 1185 (5th Cir.1977).
Finally, the mistrial on Count 11 does not bar reprosecution of the offense charged. It necessarily follows that relitigation of the factual issues underlying the charge is not proscribed. Illinois v. Somerville, 410 U.S. 458, 93 S.Ct. 1066, 35 L.Ed.2d 425 (1973); United States v. Westoff, 653 F.2d 1047 (5th Cir.1981).
III. Jury Instructions
Garza claims the trial court erred in failing to recharge the jury on the definition of “willfully” when the court granted the jury’s request and repeated the definition of “aiding and abetting.” As a general rule “ ‘the necessity, extent, and character of any supplemental instructions to the jury are matters within the discretion of the district court.’ ” United States v. Andrew, 666 F.2d 915, 922 (5th Cir.1982), quoting United States v. Braverman, 522 F.2d 218, 224 (7th Cir.1975). A conviction will not be reversed because of a trial court’s failure to give a requested instruction if the charge, taken as a whole, accurately reflects the legal issues and does not allow the jury to convict on an offense not charged in the indictment. United States v. Fischel, 686 F.2d 1082 (5th Cir.1982); United States v. Thetford, 676 F.2d 170 (5th Cir.1982). The court may decline a requested charge if it has been stated elsewhere in the instructions. United States v. Robinson, 700 F.2d 205 (5th Cir.1983).
The district court defined “willfully” in the exact language of the Pattern Instructions for the Fifth Circuit, differing only in punctuation which may have been the choice of the court reporter:
The word “willfully,” as that term has been used from time to time in these instructions means that the act was committed voluntarily and purposely with the specific intent to do something the law forbids. That is to say, with a bad purpose either to disobey or to disregard the law.
This instruction is consistent with the Supreme Court’s teachings that the term willfully in 18 U.S.C. § 242 implies conscious purpose to do wrong and intent to deprive another of a right guaranteed by the Constitution, federal statutes, or decisional law. Screws v. United States, 325 U.S. 91, 65 S.Ct. 1031, 89 L.Ed. 1495 (1945). We conclude that the court correctly defined willfully, and we find that the court did not abuse its discretion by declining to repeat this, definition when the jury requested a recharging on aiding and abetting.
IV. Sufficiency of the Evidence
In light of our findings and conclusions that the evidence overwhelmingly establishes appellants’ guilt, we need not discuss further their contentions that the evidence fails to support their convictions.
The several convictions of Ramon G. Garza and Alfredo R. Menchaca are AFFIRMED.