Thanks to one of our NMC Consultants, this exporting trick is becoming a popular trend in the New Media Center. Instead of trying to convert to a web version within Final Cut (any version), it's actually faster to export a file at current settings, then convert that single file to the web version using mpeg streamclip. Final Cut could take 45 minutes or more to do this in one step, so by doing it in two steps, the whole process usually doesn't take more than ten minutes.
When you're ready to export your your movie, choose:
File-->Export-->Quicktime movie (not Quicktime conversion)
Leave "current settings," rename the file and tell it where to save.
This makes a single Quicktime file of the finished film.
(in FCP X choose Share-->Export media, the rest of the process is the same).
Now drag the finished file into Mpeg Streamclip. Choose File-->Export to Quicktime. When the window appears, turn the quality to 100, and change the compression to "h.264". Don't worry about any other settings.
Since Mpeg Streamclip is designed to convert footage, and FCP is not, it will look better and work faster than trying to do this inside Final Cut. If the exported file is too large, or otherwise turns out to be not what you need, you can simply redo the last step, instead of having to wait 45 minutes for FCP to try again.