Pseudo-triangulations

A pseudo-triangulation is a polygon in the plane with only three convex vertices.

An interesting question about pseudo-triangulations is the following:

Is the number of triangulations of a planar point set at most the number of minimal pseudo-triangulations ?

From what I understand, this is true with equality if the points are in convex position. Herve Bronnimann talked about an experimental approach to validating this conjecture for small values of n.

p.s no wireless connection at the conference alas, so posting will be occasional.