Otherwise you will have to re-encode twice which will make quality crap.
Not necessarily. I have a habit of double encoding stuff and it's just fine. It depends on the sources you use. I have a thing about all my mp3 files being uniform in some ways. I like them all to be the same bitrate (I use 192 kbps), and to have exactly 0.5 of silence in the start and end.
So when I download stuff, I only download mp3s that are already AT LEAST 192kbps. I edit it in Cool Edit Pro - fix the amount of silence in beginning and end, do some hiss reduction if necessary, cut out any parts I do not want if the audio is too long and boring, and normalize the audio to about -3 to -6 db because the record labels make CDs too fucking loud and distorted.
After that I encode using a good encoder to 192 kbps. All my stuff sounds good, unless the original sources were crap to begin with.