"Wynona's Big Brown Beaver" is the first single from Primus' 1995 album Tales from the Punchbowl. It was nominated for the Grammy Award for Best Hard Rock Performance in 1996. Of all the band's members, only LaLonde showed up at the event. The award went to Pearl Jam for their song "Spin the Black Circle".

The song epitomizes Primus's musical eccentricities, whereby the group's signature funk metal stylings are comically inflected with a sound vaguely reminiscent of bluegrass and southern rock. During the song's guitar solos, Larry LaLonde's playing shifts from almost "noise" guitar in the first solo to a somewhat country-sounding technique and banjo-style finger-picking on the second (inspired by The Grateful Dead late singer/guitarist Jerry Garcia). The song's lyrics constitute an absurd, rambling tale about a woman named Wynona and her "beaver". They combine an on-the-surface crude sexual double entendre in "beaver" with the more purely nonsensical silliness typical of the band (e.g., strange references to baboons, Taco Bell 7-layer burritos, carnies, bumper cars, drugs and porcupines).

The band also filmed a music video for "Wynona's Big Brown Beaver", centered on the band dressed as comical-looking cowboys in costumes made of foam rubber. The costumes bore a strong resemblance to those used in a popular Duracell advertising campaign at the time which featured a family of battery-powered, toy-like people (the Puttermans). In an interview, bandleader Les Claypool revealed the suits were intended to resemble "cheap plastic cowboy action figures". The video jumps between shots of the band playing in a barn and of the band engaged in parodies of cowboy activities such as shooting bottles, riding toy horses, and playing poker among other things. The video also features some airbrushed drawings done by Claypool. The video's live action sequences were filmed at Claypool's home, known as Rancho Relaxo. The video marks the second video appearance of Les' red Fender Jazz bass.

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