I'm having trouble building my solos on piano - starting off calm, and then building it, in order to keep it interesting for longer periods of time. On other instruments (I play saxophone as well) I'd achieve the sparse simply by playing short phrases with long rests between them. This works because the rhythm section fills the gaps, however as the piano is part of the rhythm section, I can't apply the same idea to it. Does anyone have any ideas about how to improvise in this way, or links to recordings where the pianist does improvise very sparsely?
Bill Evans was the king of sparse playing in a trio context.
Five Ways to Play like Bill Evans
To get to the source of Bill Evans' technique, listen to Claude Debussy.
Without knowing exactly at which level you are I can only offer you generic solutions:
I hope it helps.