Ween now seems like a permanent fixture on the pop-cultural landscape, but when the band first hit MTV in the early '90s, their longevity wasn't so secure. Nearly two decades on, though, Aaron "Gene Ween" Freeman and Mickey "Dean Ween" Melchiondo preside over one of the most devoted cult fan bases in American music. So how exactly did Ween manage to transcend joke-band oblivion?

One answer is that, in the years following their MTV breakthrough, Ween gradually polished their output, turning their staunchly primitive musical sketches into hi-fi paintings. "Chocolate and Cheese," released...