I just wanted to add that the lady who taught the class I went to suggested we throw out the suggested number of stitches the pattern says to pick up and pick up what needs to be picked up, using the method she outlined and that I told about above. It is scary to "not follow the pattern", but once you do it is quite freeing. You should have near the number the pattern says to pick up (if you are using a pattern), but not to obsess over it too much. If you are way off you are probably doing something wrong.
Sometimes there may be a reason to have an exact number of stitches, for instance if you are adding a crochet trim that needs to worked over a certain number of stitches to fit exactly. But usually for a regular neck or for button/buttonhole bands it doesn't have to be an exact number. And if you are doing something like a K2, P2 ribbing you have to have a multiple that will work with your stitch.
I must hasten to add that she said this was the general rule, and that with this rule you should also be working with a needle 2 sizes smaller than the one you did the body of the sweater with. If your sweater is doing something different with the edging, to get a certain design look, you may need to follow the pattern exactly.