ALVIN B. RUBIN, Circuit Judge:
The district court held that police officers had probable cause to arrest a husband and wife, and that even if they did not, the officers and the cities that employed them were immune from suit. Because the police had probable cause to arrest the wife, and the officers and cities are immune from suit for arresting the husband even if they did not have probable cause, we affirm.
[402]*402I. The Facts
Associates Cash Express (ACE) is a commercial check-cashing enterprise with an office in Grand Prairie, Texas. Because ACE keeps large sums of cash at its offices, its office door is controlled by an alarm that must be deactivated when an employee enters the office before business hours and reactivated when the last employee leaves for the day. Each employee is assigned a different five-digit computer code number which she must key into an electronic device to deactivate the alarm whenever entering or leaving the office. Smith Alarm Company monitors electronically when each code number is entered.
On December 15, 1984, ACE discovered that approximately $45,176 had been stolen from its safe. The Grand Prairie police department immediately dispatched Officer Steve Courson to ACE’s premises to make a report, and assigned Detective Robert Willbanks to investigate the theft. In his report, Courson stated:
There was no sign of forced entry.... [It was] apparently an inside job.... [The suspect] had to have a key and known [an] alarm code number as well as [the] combination to the safe.... [The] suspect had to know [the] procedures of the business and did not ransack [the] business or damage any property[; he or she] apparently went straight to the safe and made [a] quick exit.... The entry at 7:32 a.m. is the suspicious time_ [Envelopes that contained checks were not opened ... and could not be seen through....
[Ms. Bennett and Parson] locked the business last night and left together. [Ms. Bennett] says [they] both put [the] money and checks inside the safe[; Ms. Bennett] locked the safe and spun the cylinder and says [the] safe was locked. [Ms. Bennett] then set the alarm code and had Parson call another [ACE] center to confirm their closing ... and [Ms. Bennett] locked the front door.
ACE instructed its director of corporate security, Orson “Bud” Harman, to conduct an internal investigation. Harman corroborated information contained in Courson’s report, and informed Willbanks:
To obtain access to the safe ..., an employee must enter an assigned computer code....;
The alarm code [number 27584] used to enter the ... office [at 7:32] on the morning of December 15, 1984 belonged to Ms. Parson, but she took and passed a polygraph exam later that day;
Ms. Bennett ... arrived late ... to work ... on the morning of December 15, 1984, ... claiming] that she had overslept and had to drop off her son with a babysitter;
After the burglary, Ms. Bennett gave us a piece of paper from her purse on which Ms. Parson’s alarm code had been written, but claimed that she had not used this code to enter the ... office on December 15, 1984. Nevertheless, the polygraph examiner stated that, in his opinion, Ms. Bennett had not been truthful in answering three of the questions she was asked during her polygraph exam; and she agreed to an appointment to take another exam and then failed to show up.
Willbanks prepared an affidavit for an arrest warrant for Ms. Bennett based primarily on Courson’s report and communications with Harman. He stated in part:
There was no sign of force on the safe or the doors [of the business]....
Officer Courson ... learned that ... [Ms. Bennett and] Parson were the last two at the business on 12-14-84 and ... they locked up ... at 8:45 p.m. ... A check with the alarm company showed the alarm ... went off at 7:32 a.m., 12-15-84....
Bud Harmon [sic] ... stated [to Detective Wilbanks] that ... [Ms. Bennett was] given three separate [polygraph] tests and had show[n] deception on each when questioned about [her] knowledge of who committed the offense and if she was involved_ [Ms. Bennett] did not come ... to take another [polygraph] test from a different operator [despite having made an appointment].... Harmon [sic] further advised that ... it was learned from [Ms. Bennett that] she [403]*403had borrowed the alarm code number assigned to ... Parsons. Parsons told Harmon [sic] that [Ms. Bennett] ... told her she could not recall her code number as she had been involved in a traffic accident recently and lost all knowledge of what her number was. Record checks revealed [sic] [that Ms. Bennett] was involved in a minor accident ... on 10-10-84[;] however no injuries were noted on the state report....
[Ms. Bennett] arrived late for work on 12-15-84 and stated she had overslept and was late taking her little boy to the babysitters_ [T]he babysitter ... advised [Detective Wilbanks] that [Ms. Bennett] did not bring the child to her home on 12-15-84.
In accordance with the practice of the Grand Prairie police department, Officer Bill Ballard signed and presented the affidavit to a magistrate, who issued the warrant. An officer of the Grand Prairie police department, who is not identified in the record, subsequently arrested Ms. Bennett at her apartment.
Both Willbanks and Harman continued to investigate the theft after the magistrate had issued the warrant for Ms. Bennett’s arrest. Relying on evidence he had collected while preparing the application for the warrant to arrest Ms. Bennett, as well as additional information provided by an informant incarcerated at Dallas County jail, Willbanks prepared an affidavit for Mr. Bennett’s arrest. It stated in part:
It was learned that [Mr. Bennett] was scheduled to travel to Mineral Wells, Texas on 12-15-84 to bid [on] a construction job....
Det. Willbanks received information there was a black male, Harold Hill, in the Dallas County jail who might know something about this offense. On 1/17/85 Det. Willbanks interviewed Mr. Hill and was told that about five days prior to [C]hristmas he was at the residence of a Stan Clark in Fort Worth and [Mr. Bennett] came to that residence to buy heroin. While at the residence, the defendant was bragging about ripping off a check cashing place in Grand Prairie where his wife worked for about $87,-000. He told Clark and Hill his wife had left the safe unlocked and given him a code for the alarm and he went in and took the cash. This information was revealed to Det. Willbanks without Det. Willbanks telling him anything about the offense.
Hill further stated that [Mr. Bennett] had supplied Clark with rent money and other cash and bragged he had plenty of money stashed and if either one needed money to let him know.... Dallas County records show [Mr. Bennett] has been arrested and convicted of armed robbery, burglary and was recently paroled from the Texas Department of Corrections for forgery.
Ballard signed and presented the affidavit to a magistrate, who issued an arrest warrant. Officer Little of the Mesquite police department arrested Mr. Bennett when she saw him stop his flatbed truck in the middle of an intersection and, after radioing Mr. Bennett’s identification to the Mesquite police department, learned that Grand Prairie had an outstanding warrant for his arrest.
After the police had arrested Ms. and Mr. Bennett, a grand jury refused to indict them. The Bennetts subsequently sued officers of the Grand Prairie and Mesquite police departments and both cities for arresting them pursuant to warrants that had issued without probable cause, in violation of their civil rights under 42 U.S.C. § 1983. The district court rendered summary judgment that the police had probable cause to arrest the Bennetts, and that even if they did not, the officers and cities were immune from suit. The Bennetts appeal.
The first issue is whether there was probable cause to arrest Ms. and Mr. Bennett.1 We find that such cause existed as to Ms. Bennett, and assume arguendo that [404]*404it did not exist as to her husband. We then consider whether any of the officers or cities involved in conducting the investigation, preparing the warrant application, or arresting Mr. Bennett may be held liable for their actions.
II. Probable Cause
Probable cause to arrest an individual exists “ ‘when the facts and circumstances within the arresting officer’s personal knowledge, or of which he has reasonably trustworthy information, are sufficient to occasion a person of reasonable prudence to believe an offense has been committed.’ ”2 A magistrate determines that probable cause exists from the totality of circumstances presented to him in the warrant application.3 We review his decision, and the police officer’s decision to seek an arrest warrant, by evaluating the facts available to the officer at the time he submitted the application.4
A. Ms. Bennett
When preparing the warrant application for Ms. Bennett’s arrest, Willbanks relied primarily on information provided by Cour-son and Harman. Ms. Bennett challenges neither the veracity nor reliability of these sources. There is, moreover, no question that the facts alleged in the warrant affidavit — if true and admissible in a warrant application — are sufficient to establish probable cause to issue a warrant for Ms. Bennett’s arrest. Ms. Bennett’s challenge is limited to Willbanks’ use of certain evidence in the warrant application — the results of the polygraph tests and allegedly false statements and misrepresentations— to establish probable cause, and to Ballard’s signature and presentation of the application to the magistrate when the facts related were, for the most part, hearsay.
1.
Results from polygraph exams are generally inadmissable at trial as evidence to determine guilt.5
“The major danger of scientific evidence is its potential to mislead the jury; an aura of scientific infallibility may shroud the evidence and thus lead the jury to accept it without scientific scrutiny.” ... [I]t is feared that the jury will overestimate [a polygraph’s] probative value, ... despite the fact that, at a conservative estimate, an experienced polygraph examiner can detect truth or deception correctly 80 to 90 percent of the time.6
[405]*405In this circuit, “the rule is well established ... that the results of lie detector tests are inadmissible in federal criminal cases”7 because they are “not yet ... accepted by the courts as a scientifically reliable method of ascertaining truth or deception.”8
Other circuits, however, have found that “[scientific developments seem to have made the polygraph more reliable” and “[s]cientific evidence ... more a part of the ordinary trial.”9 These courts have admitted polygraph results into evidence at trial when the judge “carefully circumscribe[s] the extent of the testimony concerning the polygraph exam,”10 and have permitted such evidence to be introduced at sentencing proceedings.11
The fear that a jury may overestimate the probative value of such evidence when considering an individual’s guilt or innocence — the factor that led some courts to preclude and other courts to limit the use of polygraph exams as evidence at trial — is absent when a magistrate relies on such an exam to determine whether there is probable cause to issue an arrest warrant. Unlike a lay jury, a magistrate possesses legal expertise; when determining probable cause, he is unlikely to be intimidated by claims of scientific authority into assigning an inappropriate evidentiary value to a polygraph report or to rely excessively on it.
A magistrate, moreover, may determine probable cause from evidence inadmissible at trial to determine guilt.12 The preliminary nature of the probable-cause determination, as well as the magistrate’s expertise in evaluating the evidence to reach that decision, permits the issuance of an arrest warrant on “much less evidence” than is required to convict an individual.13 Thus, “probable cause may be founded upon hearsay” or “upon information received from informants” — evidence circumscribed at trial — if “the information put forth is believed or appropriately accepted by the affiant as true.”14
Polygraph exams, by most accounts, correctly detect truth or deception 80 to 90 percent of the time.15 We, therefore, see no reason to create a per se rule barring magistrates, who may already consider information like hearsay, from using their sound discretion to evaluate the re-[406]*406suits of polygraph exams, in conjunction with other evidence, when determining whether probable cause exists to issue an arrest warrant. Absent an abuse of discretion, a magistrate may consider these results, as well as the other information, when determining whether probable cause exists to issue an arrest warrant.
Ms. Bennett challenges neither the integrity of the particular polygraph exam she took nor the qualifications of her examiner. Instead, she claims that the exam was “inconclusive because of the contradictory results,” and that Willbanks mischaracterized these results in the affidavit.
The polygraph examiner found that Ms. Bennett truthfully answered “no” to the question, “Recently, did you enter ... [the ACE office] after hours for a dishonest reason,” but had shown “[deception” and “was not truthful” (emphasis in original) when asked:
In the last 48 hrs., do you know for sure who took the missing large amount of money dishonestly from the [ACE] office?
In the last 48 hrs., did you help anyone take any part of the -missing large amount of money dishonestly from the [ACE] office?
In the last 48 hrs., did you, yourself, take any part of the missing large amount of money dishonestly from the [ACE] office?
In his warrant application, Willbanks referred to Ms. Bennett’s performance on the polygraph test as “poor,” stating that Ms. Bennett “had shown deception ... when questioned about [her] knowledge of who committed the offense and if she was involved.”
The results of Ms. Bennett’s exam were not inconclusive. Her examiner stated that she deceptively answered three critical questions, and emphasized that she was not truthful. Willbanks’ characterization of Ms. Bennett’s polygraph results reflects accurately the examiner’s evaluation of Ms. Bennett’s performance.
In addition to the polygraph material, Willbanks knew at the time that he filed the warrant application that Ms. Bennett was the last employee to leave and lock the building the night before the robbery, she possessed the entry code issued to her co-employee and actually used to enter the building at the time the robbery allegedly occurred, and her excuse that an automobile accident occasioned her need to acquire her co-employee’s code was not consistent with police records. These factual aver-ments focused suspicion on Ms. Bennett, and the results of the polygraph only corroborated her possible participation in the robbery.
2.
Ms. Bennett also claims that the warrant application contained other errors: Courson was not Willbanks’ sole source of information; neither Willbanks, Ballard, nor Cour-son contacted the alarm company; Ms. Bennett took one, not three, polygraph exams, and refused to take another test only after ACE had fired her; Ms. Bennett was hospitalized nine days after the automobile accident; Ms. Bennett took her son to the babysitter on December 15; and Ballard, the officer who signed and submitted the affidavit to the magistrate, never participated in the investigation.
Several of Ms. Bennett’s challenges have no basis in fact: in the affidavit, Willbanks identified clearly which information he received from Courson and which information came from Harman; and he never asserted that he, Ballard, or Courson had talked with the alarm company. Nothing in the record demonstrates that Will-banks made “a false statement knowingly and intentionally, or with reckless disregard for the truth”:16 Willbanks’ statement that Ms. Bennett had refused to take another polygraph exam was not inaccurate or misleading and was based on information Harman had provided; Ms. Bennett's hospitalization nine days after the automobile accident does not negate the fact that the police reported no injuries from the accident, and the hospital records [407]*407Ms. Bennett proffered do not reveal that her memory was so impaired that she needed Ms. Parson’s computer access code. Whether Ms. Bennett took one or three polygraph exams, and whether she brought her child to a babysitter on the morning of the robbery, are evidentiary details that must be evaluated with all the other evidence; they neither disprove nor establish the existence of probable cause, and are not “necessary to th[at] finding.” 17
Although he had never participated in the investigation, Officer Ballard signed and submitted the affidavit to the magistrate as if he was himself attesting to the facts recited. According to Willbanks, this is routine practice at the Grand Prairie police department.
A police department does not enhance its ability to obtain warrants by consistently submitting affidavits signed by an officer possessing no personal knowledge of the facts to which he attests. When, as here, the officer-affiant states as fact only what he has learned from another officer’s statement of what he has learned from yet two other informants, one of whom is not a police officer, the circuitous transmission of information obfuscates judicial consideration, and invites increased judicial scrutiny, of the affidavit. Police should, therefore, seek to provide magistrates with warrant applications from the law enforcement official most directly involved in the investigation and most familiar with the facts stated in the affidavit, rather than routinely reserving for one officer the task of collecting, signing, and presenting affidavits from various officers.
Nonetheless, it is undisputed that officers may submit warrant applications containing hearsay,18 including, of course, information provided by other officers.19 In this case, Ballard signed and presented an affidavit prepared by Officer Willbanks, who himself had relied on information provided by Officer Courson and private investigator Harman. Ballard thus submitted a warrant application effectively attesting to the reliability of information provided by Willbanks. Although Ballard misidentified his informant in the boiler-plate preface to the affidavit as Officer Courson, this error was later corrected in the body of the affidavit, which related what information Cour-son had supplied to Willbanks, what facts Harman had offered to Willbanks, and what evidence Willbanks had uncovered himself. Whether Willbanks or Ballard affixed his signature to the bottom of the affidavit, the magistrate’s primary task was to evaluate the reliability of the factual accounts related by Willbanks, Courson, and Harman.
There is no infirmity in the facts alleged in the warrant application for Ms. Bennett’s arrest that affect the determination that probable cause existed to issue a warrant for her arrest. The district court, therefore, appropriately dismissed her section 1983 action against the individual officers and the City of Grand Prairie.
B. Mr. Bennett
The existence of probable cause to justify the submission of a warrant application for Mr. Bennett’s arrest or the magistrate’s issuance of a warrant is less clear. There was no evidence to connect Bennett with his wife’s alleged actions, save the hearsay supplied by an informant who related that Bennett had boasted of his complicity in the course of a heroin transaction. For present purposes, we accept that interpretation of the evidence most favorable to Bennett — that the facts known to Will-banks would be insufficient under present law to give Willbanks probable cause to arrest Bennett and that the facts recited in the affidavit provided an insufficient basis [408]*408on which to conclude that there was probable cause to arrest him.
III. Official Immunity
Mr. Bennett is, however, prevented from holding the individual officers liable under section 1983 for arresting him without probable cause.
A police officer may be held liable in his individual capacity for filing an application for an arrest warrant without probable cause, the Supreme Court held in Malley v. Briggs,20
if, on an objective basis, it is obvious that no reasonably competent officer would have concluded that a warrant should issue; but if officers of reasonable competence could disagree on this issue, immunity should be recognized.... Only where the warrant application is so lacking in indicia of probable cause as to render official belief in its existence unreasonable ... will the shield of immunity be lost.... [The question] is whether a reasonably well-trained officer in [the defendants’] position would have known that his affidavit failed to establish probable cause and that he should not have applied for the warrant.21
When determining qualified immunity, the actions of a reasonably competent officer are “assessed in [the] light of the legal rules that were ‘clearly established’ at the time [the action] was taken.”22 A legal right is “clearly established” if the “contours of the right [are] sufficiently clear that a reasonable official would understand that what he is doing violates that right.” 23
The party seeking damages from an official asserting qualified immunity bears the burden of overcoming that defense.24 In this case, Bennett has failed to prove that any of the officers he has sued acted in an “objectively unreasonable”25 manner.
Officer Courson, who investigated the robbery and filed a routine report with the Grand Prairie police department immediately after it had occurred, acted as any reasonably competent officer would have acted if placed in his position. Officer Little, who executed an arrest warrant valid on its face, also acted reasonably and competently, since she was entitled to assume that the warrant was obtained validly.26 Neither officer may be held liable for any damages Bennett may have sustained.
Officer Willbanks prepared a warrant application unsupported, we assume arguen-do, by probable cause. In his affidavit, Willbanks relied primarily on information he had obtained from Hill, the incarcerated informant who said that, in the course of a heroin deal, he had personally heard Bennett brag about the robbery. Because Mr. Bennett asserts many of the same challenges to the probable-cause determination that Ms. Bennett raised, and we have already rejected these claims, the unreliability of the information Hill provided remains Bennett’s only additional support for challenging the issuance of an arrest warrant and constitutes the sole basis on which the [409]*409affidavit may not state probable cause. The determination that Willbanks is entitled to qualified immunity, therefore, turns on whether a reasonably competent officer, at the time Willbanks prepared the warrant application, would have relied on the information Hill provided.
Willbanks prepared the warrant application in January, 1985. In June, 1988, the Supreme Court decided Illinois v. Gates,27 instructing that when a warrant application contains information obtained from an informant, the informant's " 'veracity,' 'reliability,' and ‘basis of knowledge’ are all highly relevant in determining the value of his report.”28 Thus, if a particular informant is
known for [his] unusual reliability, ... his failure, in a particular case, to thoroughly set forth the basis of his knowledge surely should not serve as an absolute bar to a finding of probable cause based on his tip.... Conversely, even if we entertain some doubt as to an informant's motives, his explicit and detailed description of alleged wrongdoing, along with a statement that the event was observed firsthand, entitles his tip to greater weight than might otherwise be the case_ It is [also] enough, for purposes of assessing probable-cause, that “[c]orroboration through other sources of information”... provid[e] “a substantial basis for crediting the [affidavit].”29
Although Hill was not a reliable informant by traditional criteria and Willbanks did not corroborate the information he related, Hill did provide some details of the robbery: he described how Mr. Bennett had boasted of robbing the check-cashing business where his wife had worked, how Ms. Bennett had left the safe unlocked, and how Mr. Bennett had entered the building with an alarm code provided by his wife. Hill did not, however, submit with this information “a statement that the event was observed first hand”;30 he asserted that he had only heard Bennett boast of committing the crime.
Gates did not decide whether uncorroborated information provided by a first-time informant who had only heard an individual talk about committing a crime may, if it contains an “explicit and detailed description of alleged wrongdoing,” constitute first-hand “observation]” of “the event.” Prior to Gates, however, in United States v. Darensbourg,31 we had held that a detailed statement provided by a first-time, non-eyewitness informant whose story had not been corroborated may support “an inference that the informant gained his information in a reliable way.”32 A year after Gates, in United States v. Phillips,33 we discussed Darensbourg approvingly, without addressing whether Gates had contradicted it.34
Without determining whether the information Hill provided, together with the other evidence available to the police officers, established probable cause to arrest Bennett, we conclude that, given these precedents, Willbanks’ reliance on this information was objectively reasonable; a reasonably competent officer in Willbanks’ position may have believed that Hill’s firsthand “observation” of Bennett’s boasts of committing the alleged wrong-doing satisfied the standard enunciated in Gates. A reasonably competent officer may have [410]*410considered information derived from such post hoc observation, together with the other facts in the affidavit, sufficient to establish probable cause to arrest Bennett. The district court, therefore, properly dismissed Bennett’s claims against Willbanks.
The district court also properly dismissed Bennett’s claims against Ballard. When Ballard signed and presented the warrant application to the magistrate, he relied entirely on information Willbanks had provided. Because probable cause may be based on hearsay,35 including hearsay provided by police officers,36 Ballard’s reliance on the information Willbanks had provided is objectively reasonable. Just as an officer with “no personal knowledge of any of the facts establishing probable cause” may “carr[y] out directions to arrest given by another officer who does have probable cause,”37 so may an officer who has no personal knowledge of facts asserted in an affidavit rely on information provided by another officer to file a warrant application.
IV. Municipal Immunity
Bennett may not hold either the City of Grand Prairie or the City of Mesquite liable for his presumably unconstitutional arrest. The Supreme Court stated in Monell v. Department of Social Services of the City of New York38 that “a municipality cannot be held liable under 1983 on a respondeat superior theory”—that is, “solely because it employs a tort-feasor”— but may be held liable where “action pursuant to official municipal policy ... cause[s] a constitutional tort.”39 In his original complaint, Bennett claimed that the cities of Grand Prairie and Mesquite
approve[d] and encourage[d], through policy and custom, the illegal arrest ... in situations similar to the one herein alleged. Further, both Cities, because of improper and inadequate police department training and refusal to remove from duty police officers such as the individual Defendants, have through custom caused the harm the Plaintiffs have endured. Both Cities, knew or should have known that the Defendants were unfit to serve in their respective positions, but took no action against them and/or failed to remove them from duty and/or failed to correct or prevent their illegal actions.
While Bennett alleges that he was falsely arrested pursuant to an official municipal policy, he has failed to adduce, and the record does not reveal, any specific facts demonstrating that Grand Prairie or Mesquite showed “deliberate indifference” toward training officers,40 or that this allegedly inadequate training was the “ ‘moving force’ ”41 behind Bennett’s supposedly false arrest. The district court, therefore, appropriately dismissed Bennett’s claim against the cities on summary judgment.42
Bennett also claims, for the first time on appeal, that Grand Prairie customarily overworked and provided insufficient funds to its police department. We do not consider claims raised for the first time on appeal.
[411]*411For the foregoing reasons, the judgment of the district court is AFFIRMED.