I find holding the melodica by the strap (as shown in some of your images) to be uncomfortable and unstable, Jazzman. I cradle it, balanced, in my left hand, securing it mainly with the thumb and the middle finger. This works especially well with a 32 key melodica. Your advice against holding the instrument too tightly makes sense to me. It does seem that this would affect the sound in unintended ways. But resting the bottom in the left hand and stabilizing at the mouth also works well.