Mathematical morphology, as originally described by Matheron and Serra, consists of the application of set theoretical operations between the image set X and a structure element set B. Image skeletons are very efficient representations of shape, and can be directly derived using the morphological operations of erode and open. If done at full image resolution, derivation of a skeleton can be very time consuming without dedicated signal processing hardware. This paper presents an alternative to the standard approach that relies on morphological operations within the wavelet coefficient space. In particular, the skeleton transformation can be done very efficiently at the reduced resolution of the coarse wavelet coefficient levels. We investigate the relationship between wavelet image compression and morphological transforms for the derivation of skeletons. We also report the results of some experimental studies on binary and gray scale images.