If you've got a good voice, you're a good musician. What's all this about needing to have a musical accompaniment? Make a point of singing unacconmpanied unless you come across an accompnaist who really improves the song, which is not that common.

A lot of instrumentalists seem to find it very hard to follow the voice of a singer, especially when they vary the way they carry a tune from line to line and from verse to verse - which is how traditional singing is done more often than not. That's not "ragged", it's free. And often enough, rather than realising it is their own technique which is at fault, such instrumentalists blame it on the singer.