You might like to look at ocenaudio. It's an Audacity-style editor, but simpler and much quicker to use. In particular, if you top and tail an mp3 file a simple Ctrl-S will save it with no recoding or exporting.
I must add that, for reasons unknown, this very useful program has just stopped working on my W7 laptop, though it is running happily on my Vista media centre. Apart from this glitch it would definitely be my preferred editor (does anyone actually understand all the stuff Audacity can do?).
Another option is Wavosaur. It has many of the advantages of ocenaudio in terms of a slick UI, but it does have to recode when saving to mp3. Like Audacity, it needs a local copy of lame_enc.dll in order to export to mp3. If you use the 64-bit version, be sure to get a 64-bit version of lame, too. Again, for a simple job, I'd use this in preference to Audacity.
I personally avoid Wavepad as it's by NCH software, who are masters of the slippery business of faux-freeware. They fooled me once but I'm not getting caught again...
I've tried MP3DirectCut and while it is a seriously bizarre (stone age?) UI, it does work well and it's very fast for the task of cleaning up downloaded iPlayer files - once you get used to it.