How did Futurama have so many celebrity guest appearances?

I've been going back and watching earlier seasons, which - I thought - had a smaller budget and less recognition. But after taking a closer look at the credits I realized there's a lot of celebrity heads that are voiced by the actual celebrities. The star trek episode actually had the full original cast - and those weren't bit parts! I get that the show's a social commentary, but wouldn't it have been easier to get sound alikes? Is there a story behind the show's giant special appearances list?