A systematic study of the morphology of self-organized islands in the InAs/GaAs(001) and Ge/Si(001) systems is presented, based on high-resolution scanning tunneling microscopy measurements. We demonstrate that in both cases two main island families coexist: smaller pyramids bound by one type of shallow facets and larger multifaceted domes. Their structure and facet orientation are precisely determined, thus solving a highly debated argument in the case of InAs/GaAs(001). The comparison between the two material systems reveals the existence of striking similarities that extend even to the nature of island precursors and to the islands that form when depositing InGaAs or GeSi alloys. The implications of these observations on a possible universal description of the Stranski-Krastanow growth mode are discussed with respect to recent theoretical results. © 2005 Elsevier B.V. All rights reserved.