Why are drop shadows so hard to render, and is there an easier alternative for an aging computer?

I've been using drop shadows on a logo I'm working with and when I apply the effect it takes a good 30-40 seconds for it to finish, and then same amount of time for each edit. I'm using an older macbook here, so it's not super fast but it's no netbook either. Why are drop shadows so intensive to render, and is there something not quite as resource-heavy for improving logo viewability against a mixed-color background?