In the beguiling opening moments of “Spider-Man 2,” we learn that Peter Parker is not just a freelance photographer now but also a delivery boy with seven and a half minutes to get a stack of pizzas 42 blocks uptown. Peter makes a go of it on his moped, encounters gridlock, then busts out that cool Spidey suit and delivers the damn things swinging by one hand. He’s late anyway. In short order, Peter gets fired; threatened by his slum-lord; chewed out by his physics professor; slapped by his brooding buddy Harry (James Franco) for not telling him who Spider-Man is so he can avenge his father’s death, and scolded by his beloved Mary Jane Watson (Kirsten Dunst), who’s so sick of trying to solve the mystery of who he is that she’s hooked up with an astronaut. Plus, he washes his Spidey suit at a laundromat and the colors run and ruin his boxers. All this is by way of telling us that it’s hard to be Spider-Man and have any kind of life at all. Peter decides to hang up his tights so he can win back Mary Jane. Then a scientist he idolizes, Dr. Octavius (Alfred Molina), goes berserk and threatens Manhattan with a gonzo fusion experiment.

There have been so many movie villains menacing so many people for so long that some grown-ups’ eyes will glaze over the minute Dr. Octavius goes mental. Still, Molina’s character, as well as his performance and the attendant effects, is far more interesting than Willem Dafoe’s grating, over-the-top turn as the Green Goblin in the first movie. (Dafoe, don’t ask how, shows up in a cameo late in the sequel–and still appears to have bits of scenery stuck between his teeth.) In any case, Maguire and Dunst are the real attraction. They look gorgeous, and their chemistry is deeper, quirkier and utterly convincing, partly because they’re such unshowy actors–one of the ironies of “Spider-Man” is that it’s made a swinging superhero out of a guy who acts only with his eyes–and partly because they haven’t gotten so famous that they’ve ceased to be interesting.

For a man directing a Fourth of July movie, Raimi spends an unusual amount of time letting emotions have center stage, often in scenes between Peter and his Aunt May (the great Rosemary Harris). Kids in the crowd may occasionally get restless for action, but you’ve got to admire the filmmakers for expecting more, rather than less, of their audience, and for hunting for the highest common denominator. And it’s not as if the action sequences don’t deliver. The new movie’s climax, which involves a runaway subway train and evokes a kind of communal heroism without pandering, outdoes the original in a way that only Spider-Man could: by leaps and bounds.