One thing I've done that works fairly well is to make the first stitch one stitch shorter than what's called for.
So, for example, if you are working in dc, the first stitch on a new row (the starting stitch) would be a ch 2 rather than a ch 3. For a hdc, it would be a ch 1. Note that you may have to make these chains a little looser than normal--the idea is to get the stitches up to the desired height without creating the hole that the original called-for stitch does.
Lily Chin then suggests that rather than counting these chains as your first stitch, you should go ahead and make the actual stitch (dc, hdc, or whatever) into the first stitch. Just be careful on your next pass not to count the chain stitches as a stitch!
You might try this and see how it works in the round.
I *think* I've just used the shortened chain as the first stitch, though, without problems, but try it both ways and see what you think.