When a firefighters' union resorts to deceitful political stunts, it squanders the respect and credibility its members have sacrificed so much to earn.

Which is why firefighters, more than anyone, ought to be livid over their national union's shamelessly mendacious new video skewering former Mayor Rudy Giuliani for his handling of the attack on the World Trade Center.

Let's be clear: No one has a higher regard for The Bravest than we do.

No one.

Their record of heroism on 9/11 - and, indeed, every day of the week - is unassailable.

But, as Giuliani himself has said, firefighters have no "monopoly on caring" about the 343 of their members murdered in the attack. And their union's attempt to milk public support, sympathy and gratitude - in the name of some bargain-basement political cause - is simply despicable.

Nor, it must be said, is the public record of the FDNY heroes since that grim day entirely blemish-free.

Recall the near-riots that broke out when Giuliani - out of concern for the safety of firefighters, no less - tried to order some of them off the pile.

Remember the shoving and punching and throwing of objects - followed by the arrest of 18 firefighters, including one for striking a police officer.

Recall their resistance to wearing protective equipment during the rescue and recovery efforts at Ground Zero.

Yes, such behavior reflects their selfless commitment to their brethren and to finding their remains. Yes, to a degree, that's admirable.

But a failure to accept instructions could have put their safety and health - and that of others - at considerable risk, given the dangers at the site.

Meanwhile, the more than occasional fistfights between firefighters and cops - sometimes even at the scene of emergencies - are legendary.

New York's Bravest, and their leaders, have also had differences with Giuliani on a host of non-9/11 issues - not least, his decision to make cops higher in the pecking order when emergency-response and security issues arise.

But none of this excuses the blatant lies in the video released last week by the International Association of Fire Fighters. The flick all but holds Rudy responsible for the attacks themselves.

What's the union's beef, specifically?

It calls the idea that Giuliani provided leadership during the crisis an "urban legend." And says because of him, firefighters' radios didn't work and human remains were left in the debris.

These are vicious falsehoods, of course. Which is why Lee Ielpi, a former firefighter whose son died in the attack, and former Office of Emergency Management Commissioner Richard Sheirer, called the film a "disgrace."

"I was there. I saw it," said Ielpi, who worked at the cleanup at Ground Zero. "I'm not going to let lies like this go."

Here's the bottom line: On 9/11, New York was a safe, secure, well-run place - one that had been turned around, miraculously, from the chaotic, virtually lawless climate that prevailed before Giuliani took office.

Indeed, the restoration of order and renewed investment in the city helped Gotham withstand the attack in 2001 and spring back quickly.

Imagine if Giuliani's predecessor, David Dinkins, had been running the city up to, during and after 9/11. Dinkins, as mayor, took three whole days merely to end the Crown Heights riot. (Indeed, it took a physical threat against him by rioters for him to act.)

Meanwhile, Giuliani deserves every bit of praise for his leadership in the weeks after the attack. Not just for conveying confidence and calm, but also for assuring a smooth continuation of city government, despite huge obstacles.

And, of course, for running the most complex rescue, recovery and clean-up operation in U.S. history.

No one should be surprised that the IAFF is looking to impeach the integrity of a leading Republican presidential candidate. It has a record of supporting Democrats, like John Kerry and Hillary Rodham Clinton. Count on the union's endorsement of a Democrat for president next year.

But that's a pathetic reason to distort the truth and rewrite the facts about a sacred period in U.S. history. IAFF leaders owe it to their fallen brothers at least to be honest about that awful day.