Deerhoof’s journey from unpolished rock to adored indie-rock gem is baffling and circuitous. Since forming in San Francisco in 1994, the group has wandered through numerous incarnations of fragmented rock, bellicose noise, saccharine pop, and arty sound experiments. It has only been in the last three years, in which Deerhoof has released three albums, that the band has honed its still emerging signature rustle: a surprisingly bewitching mix of self-conscious rock and twee pop, two of the ’90s most stripped-mined sounds. The band has not only slyly and seamlessly combined such divergent vibes into a coherent whole, it has also managed to create music that is, most oddly, absolutely affable. The band streamlines its accessibility even further with its new album, “Friend Opportunity” (Kill Rock Stars), and in its live show, which comes to Irving Plaza on Friday.

The band’s newfound lucidity is likely the result of becoming a trio since the departure of second guitarist Chris Cohen, who left to focus on his own band, The Curtains. Mr. Cohen had joined Deerhoof for its 2002 tour to support the gleeful studio album “Reveille.” Those songs were the result of lineup changes, too, when founding guitarist Rob Fisk left the band in 2001 and the remaining members, bassist/vocalist Satomi Matsuzaki and drummer/keyboardist Greg Saunier, recruited John Dietrich. Mr. Dietrich’s slashing, multilingual guitar acrobatics meshed beautifully with Mr. Saunier’s beefy, if schizophrenic, time-keeping, a combination that practically reinvented the band as one with as much rock muscle as cutesy experimentation. Since “Reveille,” Deerhoof has blended those elements in invigorating and sometimes daft ways. The addition of Mr. Cohen in 2002 was, in part, meant to achieve the physical oomph of “Reveille” onstage.

Since then, the band’s live show has grown into a visceral punch, thanks in large part to almost constant touring. During Deerhoof’s tours behind 2003’s “Apple O’,” 2004’s “Milk Man,” and 2005’s “The Runners Four,” it was possible to catch Deerhoof in the city two and sometimes three times a year. Each successive show grew in force as the band discovered ways to turn its precocious, even fey songs into thundering rock with thick riffs — however unconventional those riffs may have been.

Deerhoof’s neatest trick, however, is how it has made its unconventionality its most endearing trait. As with a good deal of ’90s underground rock, Deerhoof’s melodies sound like standard hooks fed through a blender and reassembled without patching up all the ripped edges and missing segments. Of course, those jagged edges are usually smoothed over with technical sophistication, constructing whirligig noise segments, serrated guitar tones, and skittish rhythms into unorthodox building blocks for sing-along pop. All of these obtuse parts gel on record and onstage, as Mr. Saunier pounds away like a metalhead, Mr. Dietrich’s slices through an arsenal of distorted weapons, and Ms. Matsuzaki — whose upper register hovers between opera soprano and dog whistle — hops around onstage like a sugar-primed kid at recess.

If “Friend Opportunity” is any evidence, Mr. Cohen’s departure hasn’t toned down Deerhoof’s safe weirdness one bit. The trio is just as eccentric, only more focused about it. All of its idiosyncrasies remain — from the splintered melodies (“Cast Off Crown”) to the juvenilia gone bizarre lyrics (“If I were a man and you a dog / I’d throw a stick for you” in “Kidz Are So Small”) — in tighter, more ordered compositions. In fact, “Friend Opportunity” sounds indelibly like a Deerhoof album, but, with 10 tracks in less than 40 minutes, it’s also the band’s most unabashedly pop album.

Opener “The Perfect Me” kicks off with an eruption. Mr. Saunier’s big beats and Mr. Dietrich’s darting chord punches surround Ms. Matsuzaki as she chirps a kid’s-eyeview of friendship. A cavalcade of trumpets pepper “+81,” a summery burst of incoherent indie-pop, while on “Matchbook Seems Maniac” and “Choco Flight,” Deerhoof peels off serenely pretty webs of gossamer pop. With standout track “Believe E.S.P.,” the trio pulls off the complete antithesis of its scatterbrained approach: It gets downright funky.

There’s no telling how the band plans to tackle its back catalog as a trio onstage, but “Friend Opportunity” makes one thing sparkling clear: The new Deerhoof is the old Deerhoof — only more so.

Deerhoof plays Irving Plaza January 26 (17 Irving Place, between 15th and 16th streets, 212-777-6800).