I like turning a morse taper on the wood billet and inserting the wood billet directly into
the head stock bore. On shorter spindle pieces the morse taper will hold the piece securely
enough to part the spindle off on the tail stock end and proceed with light sanding while it
is still seated in the morse taper. You can then part the piece off from the head stock and
clean the bottom up on a belt or disk sander. This method provides the largest amount of
clearance when turning small pieces between centers.
The spring loaded drive centers also work great for spindle work and prevent the potential
splitting of the grain which can happen with solid drive point centers. Depending on the diameter
of your spindle piece these also provide good clearance for working the piece.