There are a lot folks on here who are better qualified to answer this. But, what I want to know is how (what program) are you using to convert the wav to MP3?
And, what bitrate are you converting to. I think a lot of MP3s are at 128kb. Which you will hear "artifacts" in the sound. If you can raise the bitrate up it will definitely help.
I usually convert wav files to MP3 at 320kb. They really do sound better at a higher bitrate.
If you can, give that a try and see what you think.