Divergent natural selection has been shown to promote speciation in many taxa. However, although divergent selection often initiates the process of speciation, it often fails to complete it. Several time-based, geographic and genetic factors have been recognized to explain this variability in how far speciation proceeds. We review here recent evidence indicating that variability in the completeness of speciation can also be associated with the nature of divergent selection itself, with speciation being greatly promoted by (i) stronger selection on a given, single trait (the 'stronger selection' hypothesis) and (ii) selection on a greater number of traits (the 'multifarious selection' hypothesis). However, evidence for each selective hypothesis is still scarce, and further work is required to determine their relative importance.