Staying in tune up the fret? Challenging . . .

Hi All,

I can tune my instrument so it is solidly D-A-d -- but I notice that as I move up the fret board that my notes are often a bit off. DH suggests that the action of the dulcimer (height of strings off the fret) may be contributing. But I like the feel of things as they are - and suspect it has more to do with "operator error".

What's the best way to have notes stay in tune as one frets?