Thanks Kurt,
I solved the problem by turning on polygon border edges and seeing that whenever I extrude an edge (on a Mac in Maya 6), the extruded edge is a border edge. I experimented with extruding a primitive polygon cylinder and had the same border edge result. So the answer is to merge vertices back enough along each edge, so that the edges are not border edges, just plain edges that can be deleted. Hope that helps someone out there,
Scott