Saturday night wasn't Regina Spektor's first time on stage at the Tower Theater, but her fortunes have risen substantially since her last appearance, when she opened for the Strokes in 2003. "That was my first show on my first tour," she recalled between songs. "Those guys were great. They still are."

Her erstwhile tourmates, who played some of the first shows outside New York in tiny Philadelphia clubs, rose quickly and fell nearly as fast, but Spektor's climb has been a more gradual one. Where the Strokes behaved like rock stars even in front of an audience a few dozen strong, Spektor still has the air of a precocious piano student, playing for the crowd's approval and gushing when she gets it.

The Russian-born daughter of a music professor, Spektor is a prodigious player and singer, but for the most part she lets her full talents loose in isolated flourishes rather than unbridled torrents. "Small Town Moon" — which, like a third of the evening's songs, was taken from her album What We Saw From the Cheap Seats, due out at the end of the month — ebbed and flowed, switching fluidly from a languorous melody to a triple-time recapitulation of the theme. On the chorus of "Fidelity," she sang a syncopated staccato melody while playing crisp eighth notes on the piano, a double act that might have been dizzying had she not absorbed it so thoroughly as to make it seem offhand.

Spektor's precocity can shade into preciousness. For "Oh Marcello," another new one, she opened each verse in a mock Italian accent, while the a capella "Silly Eye-Color Generalizations" was as grating as its title suggests. At their worst, her songs feel self-congratulatory, inviting the audience to join in a celebration of their mutually understood cleverness.

For the most part, What We Saw... puts Spektor's tricky tendencies on hold. In spite of its Francophone chorus and embedded Nina Simone nods, "Ne Me Quitte Pas (Don't Leave Me)" boils down to a simple simple lover's plea, and "How" does away with subterfuge altogether, asking simply, "How can I forget your love?" Poets have spent thousands of years trying to answer that question, and Spektor comes no closer, but there's a bravery in admitting the things you don't know, and not just showing off the ones you do.