Let T_S be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph where two members T and T^′ of T_S are adjacent if T intersects T^′ only in points of S or in common edges. We prove that the diameter of is O(logk), where k denotes the number of convex layers of S. Based on this result, we show that the flip graph of pseudo-triangulations of S (where two pseudo-triangulations are adjacent if they differ in exactly one edge—either by replacement or by removal) has a diameter of O(nlogk). This sharpens a known O(nlogn) bound. Let be the induced subgraph of pointed pseudo-triangulations of . We present an example showing that the distance between two nodes in is strictly larger than the distance between the corresponding nodes in .