Granted, it's easy to get confused about a mock-arty-garage-polka-metal-country rock duo whose very name implies uncertainty: They Might Be Giants. Given that situation, John Flansburgh, the bespectacled Giant, would like to set the record straight about the band's purpose. "We like playing fun rock music, for the love of it," says Flansburgh, 28. "We only pretend to have a plan for world domination." That windy sound you hear is, no doubt, Mikhail Gorbachev breathing a sigh of relief. But the Giants are serious about not taking rock seriously. "Rock is just about the biggest dinosaur around," says co-Giant John Linnell, also 28. "It's nice to listen to, but it's got this bloated aspect to it that has to be deflated."

Their opening salvo against the corporate rock monster was last year's They Might Be Giants LP, a 19-song cannonade fired by a popgun—tiny, New Jersey—based Bar/None Records. Forty-three minutes of quirk rock that veers from the ridiculous ("Youth culture killed my dog...the hip-hop and the white funk just blew away my puppy's mind") to the more ridiculous ("There's only two songs in me and I just wrote the third"), the album has generated good reviews ("hyperverbal and seriously funny," quoth the New York Times), a strong cult following and 100,000 sales. Okay, okay; as Linnell says, "That doesn't sound like much in a Van Halen world." But it's not bad for two guys who wear four-foot-tall fezzes onstage and market their music by playing snatches of new songs on a telephone answering machine (718-387-6962). When pressed, the Giants admit to sincere attempts at pop craftsmanship—"There's strong melody in most of what we do; it's our secret weapon," says Flansburgh—and are also quick to point out the importance of their tape-recorded rhythm tracks. "At first we taped because we couldn't afford a live drummer," says Linnell. Adds Flansburgh: "Now we do it because we can use strange rhythms and not worry about the drummer's head exploding."

The Giants grew up, to normal heights—Linnell is 5'10", Flansburgh 5'11"—in Lincoln, Mass., and were childhood friends. "We grew long hair in 1968 and became [8-year-old] hippie children," Flansburgh says. "Then we cut it in 1977 and joined the punk people." Linnell, whose father is a psychiatrist and whose mother is a poet, spent a year at the University of Massachusetts and three years with a band called the Mundanes. Flansburgh, whose father is an architect and whose mother founded Boston-by-Foot tours, played in several "hobby bands" and earned a B.F.A. in printmaking from Brooklyn's Pratt Institute.

When the pair coincidentally moved into separate apartments in the same Brooklyn building on the same day in 1981, they decided fate meant for them to take a Giant step. Billed as "El Groupo de Rock and Roll," they debuted before 30 non-English-speaking Sandinista supporters at a 1982 rally. By 1984 they had lifted their current name from a 1972 George C. Scott movie about a lawyer who believes he is Sherlock Holmes.

Supporting themselves with "slave jobs"—Linnell was a bike messenger, Flansburgh a people counter in Grand Central Station—they played "the lowest rung of Manhattan clubs" before developing the kind of following that allows them, nowadays, to afford to stay at Motel 6 when they tour. Both Giants regard the typical rock star excesses—cheap women and expensive cars—as shallow, decadent and, lamentably, out of reach. "We're willing to sleep with beautiful women," says Flansburgh hopefully (the Giants are single). "Ah, the Crüe, they're livin' the dream," adds Linnel, with perhaps less than perfect sincerity.

Doggedly pursuing their own slightly skewed dream, the Giants have just released a five-song EP (She Was a) Hotel Detective and are about to embark on a West Coast tour, which may increase public comprehension of their world view. "As hard as it is to explain the band, audiences get it right away," Flansburgh says. "They don't go, 'Oh, you're just like Mick Jagger.' They go, 'Oh, you're just like my brother.' " And even if TMBG doesn't kick Van Halen off the charts, they have already begun to nudge at least one top pop star. "They Might Be Giants is available now in shopping mall record stores, under the Ts," Flansburgh says with pride. "Right next to Tiffany."