If our cynical, wisecracking age can withstand it, “What Women Want” is one of the best arguments for the return of the musical.

Mel Gibson’s newest comic venture is straight out of pre-1965 Hollywood cinema. As Nick Marshall, the grown-up son of a Las Vegas showgirl (or showwoman, as the case may be), Gibson plays a ladies’ man weaned on cocktails and Frank Sinatra lullabies. Surrounded by buxom women in tassels and Mafia chauvinists in his tender years, the charismatic yet egomaniacal ad man is indeed the product of his upbringing. So when he inadvertently establishes a psychic network with women far beyond what Dionne Warwick could ever dream, he enters a universe he never knew existed.

Incidentally, “What Women Want” has been done a disservice by its trailers, so close your eyes if they flash by on your television or theater screen. It parades the crassest lines and boils the psychic-link scenario down to a puerile gimmick, like those X-ray glasses advertised in the back of old action-adventure comic books. Rather than the coyness of a sledgehammer, director Nancy Meyers instead sustains a funny and clever momentum out of what could have been sheer farce.

From the start, Sinatra’s vocals lay down the finger-snapping, toe-tapping rhythm as Marshall quickly establishes himself as the classic arrogant charmer who needs Doris Day or Ginger Rogers to take him down.

At the coffee shop, he jars a comely woman’s coffee so he can dab at the stain on her chest before he hits on the counter girl, Lola (Marisa Tomei). He barrels through the ad agency late with a twinkle in his eye and an obscene (and misogynist) joke on his lips. In between displays of this behavior, we see his ex-wife (Lauren Holly) getting ready for her second marriage, and talking to her bridesmaid about her first husband: He’s a man’s man, which means “he’s the kind of man who doesn’t know what women want.”

Besides celebrating his ex-wife’s wedding day, Marshall has a champagne bottle primed and a celebratory lunch reserved with co-worker Morgan (Mark Feuerstein) because he thinks he’s getting the job of creative director. What the brain behind the bikini beer ads hasn’t realized is that in the last decade, the industry has become a women’s marketplace. The 16- to 24-year-old female segment, says big boss Dan Wanamaker (Alan Alda) in a meeting with Marshall, is the fastest-growing consumer group in the country. “If we don’t evolve and think beyond our natural ability,” he says, the company is doomed. That’s when Wanamaker hits below the belt: He’s hired a woman for the job.

Sabotage, of course, becomes Marshall’s blood-and-testosterone mission, even when it turns out that the fabled “man-eater and bitch on wheels” Darcy Maguire (a tanner and blonder Helen Hunt) is a collaborative, straight-talking and sensitive boss.

The moment of his transformation comes during a homework assignment when he is trying out an array of women’s products. Men in pantyhose and nail polish have been done before, but Gibson pulls it off with his gritted-teeth gamesmanship fueled by his desire to beat Maguire. The accident that sends him to the other side is one of the best-shot scenes.

When he first realizes his gift the next day, the babble of feminine noise overloads his mental circuits. Marshall’s bewilderment and horror both ring true and are the wellspring of much hilarity. His bumbling attempt to use his new power in the first creative meeting shows that he still doesn’t know how to listen, even if he can overhear women’s thoughts. It takes his marriage/family therapist (an uncredited cameo by Bette Midler) to tell him, “If you know what women want, you can rule.”

Familiar and comfortable, “What Women Want” delights, mainly because of how Marshall finds out what a goombah he is with women, including his 15-year-old daughter, and how he slyly wriggles into their good graces. The inevitable moment of self-discovery in bed happens with Lola it’s one of the movie’s highlights as Marshall struggles to perform while hearing her critical running commentary. As for the musical numbers, Gibson although built more like Gene Kelly does a soft-shoe tribute to Fred Astaire, reprising the famous coat rack dance. The rest of the time, the soundtrack of Sinatra and Alanis Morissette subs in for rousing song-and-dance numbers.

With Gibson playing the mind-reader and often anticipating what a woman says, Hunt’s character truly is more of a vessel, sweet as she is (too sweet, considering she’s in the ad business). Also, despite Marshall’s well-paced evolution, resolution of the loose ends is crammed into the last 20 minutes. That’s typical of the old formula romantic comedies, but nowadays it feels forced, and unfortunately that keeps Meyer’s production from the level of a Billy Wilder film.

By the way, I’d also hesitate calling this a woman’s film, since Gibson even while he’s channeling truly is the focus, the eye and the voice. If that’s your thing, this alone should provide for an engaging post-screening discussion.

Either way, it’s worth the price of admission. You’ll just have to provide your own singing and dancing afterwards.