DAVE LETTERMAN's Monday-night apology for a late-night rotten joke seemed sincere, but part of his explanation is questionable and how he came to his epiphany is memorable.

The crude joke - suggesting that Yankee All-Star Alex Rodriguez "knocked up" Sarah Palin's daughter during a Yankees game - released the furies, starting with Palin supporters, but quickly sliding across the political spectrum. The joke even got Dave into the National Organization for Women's Media Hall of Shame.

Last week, Letterman had offered a limp semi-apology, but the protests didn't go away. I don't know if there's anyone big enough at CBS to demand that the multimillionaire comedian get on his knees, but Monday night he did. Palin accepted the apology, but a couple of things still play in my mind.

"I had no idea that anybody was at the ballgame except the governor, and I was told at the time that she was there with Rudy Giuliani," Letterman said about midway through his apology, which got its own four-minute segment bracketed by commercial breaks.

But his apology started like this: "There was a joke that I told and I thought I was telling it about the older daughter being at Yankee Stadium . . ."

The two statements are contradictory. He either thought only Palin and Giuilani were at Yankee Stadium, or he thought Bristol, the 18-year-old, was there.

The joke would have been absent any touch of class even if Bristol had been at the Yankees game.

Letterman took the blame, as he should, but this was lousy research by his staff - confusing the two daughters. One reason the joke touched off a firestorm is Letterman's palpable, personal, political dislike of Alaska's governor (even though I think, from things he has said, that she gives him a secret, sexual itch).

Would Letterman, under any circumstances, make a similar crack about the Obama daughters, Sasha and Malia? How would Letterman feel about some kind of a child-molester joke involving his 5-year-old son, Harry?

Letterman's joke brought back memories of a puerile "Saturday Night Live" skit mocking Chelsea Clinton's plain physical appearance when Bill was president. A righteous uproar ensued.

Here are two sad cases, one ridiculing the child of a conservative, the other the child of a liberal. It is vicious, wrong and impermissible in the public media. Barf like that belongs on blogs.

Letterman apparently felt that last week's half-hearted apology was sufficient until - and this speaks volumes - he heard liberal commentator Mark Shields describe the joke as "indefensible" on the "NewsHour with Jim Lehrer."

Boing!

Dave, it seems, listens only with his left ear. Hearing it from a liberal warhorse is what snapped Letterman out of his coma of contentment. Shields got him to smell the coffee that all the e-mails, hate mail, calls for his firing or censure had not.

"Now I'm beginning to see what the problem is here," Letterman said in his apology. "It's the perception rather than the intent. It doesn't make any difference what my intent was, it's the perception."

He didn't define his "intent." To simply make a joke? To humiliate Palin? To attack the daughter? To abuse conservatives? Probably the first, but it was both dumb and indulgent.

On air, Letterman likes to play the "dumb guy," but after a transplant from his native Indiana to Connecticut, I believe he fancies himself a closet intellectual.

Proof? He watches "Newshour with Jim Lehrer."

Like "SNL," Dave now knows that grown-ups aren't allowed to pick on kids, not even for a joke. *

E-mail stubyko@phillynews.com or call 215-854-5977. For recent columns: