IN November 1991 Nirvana’s “Nevermind” was beginning its climb up the charts. The album had not yet sold more than 10 million copies, had not yet knocked Michael Jackson out of the No. 1 slot on the Billboard album chart, had not yet become the defining moment of the alternative rock movement or given Kurt Cobain the “voice of a generation” status that would help prove his undoing.

Already, though, the band’s newest member, the drummer Dave Grohl, was expressing his concerns about the impact that the album would have on his future. “Everyone is always asking if I’m afraid of the band’s success going too far,” the 22-year-old told Rolling Stone, in the band’s first interview with that magazine. “That doesn’t really make any difference. I just don’t want to be David Grohl of Nirvana for the rest of my life.”

“What a spoiled brat,” Mr. Grohl, now 40, said with a laugh when that quotation was recently read back to him. “But I think any musician would say the same thing  there’s a lot of ground to cover, a lot of work to do. I wouldn’t want to be tied down to one project or defined by any one thing.”

The odds, however, were certainly stacked against Mr. Grohl’s leaving a legacy beyond his role in Nirvana. The trio became the biggest band in the world for a time, then ended in horribly dramatic fashion with Cobain’s suicide in 1994. Mr. Grohl, who was known for having a personality as laid-back as his drumming was explosive (“He’s so easygoing, always fun to be around,” the band’s former bassist, Krist Novoselic, said in an e-mail message), was now permanently linked to one of rock’s most public tragedies.