The Bad Plus, an acoustic piano jazz trio, performed Saturday at the Hamilton in Washington. (Josh Goleman)

When the Bad Plus played its first D.C. gig, at Blues Alley in 2001, the band was the new big thing in jazz — but also something of a novelty. Here was an acoustic piano trio covering Nirvana, Aphex Twin and Blondie, both having a sense of humor and being serious about it.

They did their own original stuff, too. And now, 16 years later, on the farewell tour of their original incarnation — pianist Ethan Iverson leaves at year’s end, to be succeeded by Philadelphia’s brilliant Orrin Evans — it was the quirky, distinctive originals that dominated the Bad Plus’s set Saturday at the Hamilton. And it was a pop cover that sneaked in among Iverson, bassist Reid Anderson and drummer Dave King’s imaginative offerings.

Not that TBP’s take on Cyndi Lauper’s “Time After Time” was some palate sweetener, a commercial complacency meant to mislead the audience. It was as idiosyncratic as anything else they played, moving in a kind of casual drunken slink that the three created together. Still, it was Iverson’s solo that dominated, expressing a certain labored feel that the pianist also physically communicated by lurching back and forth on his piano stool.

Still, token or not, “Time After Time” was sandwiched between six originals, two each by King, Iverson and Anderson. These encompassed as much musical knowledge and understanding as the trio’s whole book of pop tunes. King’s “1979 Semi-Finalist,” for one, combined baroque harmonies, smashing rock beats and the same clockwork precision that made the band’s 2001 cover of Aphex Twin’s “Flim” work. On Iverson’s “Mint,” the band plumbed the depths of jazz’s avant-garde visionaries: King held down a groove that was both swinging and intermittent, evoking early Ornette Coleman, while Iverson touched on the unique harmonic language of pianist Ran Blake. Anderson’s “Big Eater,” meanwhile, was a fully processed blend of torrid phasing, tenuous harmonies and blocky yet seductive melody.

Iverson has become a go-to pianist and acclaimed blogger; King is a prolific and inventive bandleader. Anderson, though he’s become the band’s master of ceremonies, may be the Bad Plus’s least visible member — but he’s quietly among the best working bassists in jazz. His smart, voicelike four-bar fills on “1979 Semi-Finalist” made that point gorgeously. His work on Iverson’s “Mint,” holding the pulse implacably while Iverson and King tricked the ear into thinking it heard free-form time, drove it home. That knowledge makes the dissipation of the Bad Plus’s three-way chemistry a drag, but it promises that the new dynamic will be fascinating, too.