I have been playing for most of my 43years, mainly pop, rock and standards . . . for the past few years I have taken a sharp turn, or maybe a natural progression, towards staight ahead jazz based on standards and the classic jazz rep. Although having never had any training in theory, I have come to realize that I can improvize quite naturally as I visualize the chord patterns speading out in my right hand via the melody. At this point my right hand can easily run down the keyboard . . . the challenge is moving upwards towards the higher notes. Can anyone suggest a fingering exercise to strengthen this very needed aspect.

Thanks in advance!

Moving up how? in stepwise motion or leaps? I would recommend practicing scales and arpeggios in all keys, starting with one octave, then 2, 3 and then 4 octaves. Do ascending and descending.

If the problem is specifically upward, while downward goes fine, then it's got to be technical on the physical side. How about the fact that you have to cross over your thumb in one manner upward, but in another manner downward? Have you tried taking it apart in slow motion both directions doing scales and see where you're hung up?