HOUSTON --Seven of the Houston police officers on the tape seen beating Chad Holley were fired for what the police chief saw then and what you saw for yourself on ABC13. But in Houston, firing a police officer doesn't always mean they stay fired, so now we're focusing on Houston police discipline and how many fired cops get their job back and why. When faced with the video, Houston Police Chief Charles McClelland fired six of his officers, saying he couldn't trust them anymore. But two of the three appealed their firing and won. One former chief tells us you are the losers when that happens since they're not certain who's right and who to trust. Now that the video's out, you can decide. Officer Gaudencio Saucedo kicked Chad Holley once in the legs. McClelland fired him, saying it brought embarrassment to the department. Months later, a civilian arbitrator based in Dallas disagreed, changing his firing to a written reprimand. Officer Lewis Childress kicked Holley's hands long after other officers surrounded the suspect. The chief fired Childress, too, saying that makes every police officer's job harder. But without even hearing evidence, an arbitrator reversed Childress' firing on a technical timing issue. Senior Police Officer Phil Bryan was fired too. Bryan drove the car that clipped Holley, then gets out and kicks and hits Holley. Bryan was the third officer to appeal his firing -- and the only one so far to lose. HPD's had that kind of discipline record for years. "For about 15 years, about a third of the cases that actually went to arbitration were overturned in their entirety, about a third were upheld in their entirety and a about third were modified," HPD's lawyer Craig Ferrell said. Think about that. Someone outside the Houston Police Department overrules our police chief two thirds of the time. "It ought to call into question the judgment that's being made at HPD," said Aaron Suder, a police union lawyer. But Houston Councilman C.O. Bradford was Houston's police chief for seven years, and while he supports an appeals process, he says the chief should have the final word. "The police chief should get the last say so in who works for the Houston Police Department," Bradford said. This isn't a challenge Houston faces alone. We looked for examples of this across the country and even when incidents like this are videotaped, and arbitrators are overturning other police chiefs about as often as they do Houston's. In Philadelphia in 2008, eight officers kicked and hit suspects on a street corner. A Philadelphia arbitrator put them all back on the job and they gave them back pay. "They need to get these guys off the force," a Philadelphia protester said. When a Chicago professor looked at the system in that city, he found arbitrators reverse police chief discipline decisions 49.8 percent of the time. "Arbitration by its very nature is designed -- in my opinion -- to do more splitting the baby than it is necessarily pure justice," Ferrell said. "They kinda split the difference to try to make both parties happy and I think that's not proper," Bradford said. But it's our system and it's not going away. It's played itself out for years. It is playing out now, and the mayor is not happy about it. "We fired them. We intend for them to stay fired," Parker said. "Arbitrators, in two of the three situations that have been arbitrated, have said that they need to return to the Houston Police Department. We are going to fight that every step of the way." Houston police say their stats are getting better keeping fired officers fired. There are three cases left to appeal. We'll watch. One arbitrator in the case says he decides only based on what he hears, not to balance any long term record.