Arranging and Rewriting Other People's Songs

Alex was asking about rewriting Our God Reigns and it was pointed out that you can't redo all the verses without getting into issues of copyright. I think I wouldn't want to go that far.

However, should we use the songs exactly as they come in songbooks or is there some latitude? I can think of several songs that I have rearranged based on recordings by the artist or how I have heard them perform it. We sometimes add little tags, in the same way that the original artists do at concerts, which may be either spontaneous or arranged. I've even written out new music at times when there is a notable discrepancy between the dots and what we sing and what we sing sounds alright.

How much rearranging do you do and when do you think it crosses the line from valid craftsmanship to defacing someone else's work?

Wulf