Speciation and extinction rates can be estimated from molecular phylogenies. Recently, a number of methods have been published showing that these rates can be estimated even if the phylogeny is incomplete, that is, if not all extant species are included. We show that the accuracy of such methods strongly depends on making the correct assumptions about how the sampling process was performed. We focus on phylogenies that are incomplete because some subclades (e.g., genera and families) are each represented as a single lineage. We show that previous methods implicitly assumed that such subclades are defined by randomly (or in an extreme deterministic way) choosing the edges that define the subclades from the complete species phylogeny. We show that these methods produce biased results if higher taxa are defined in a different manner. We introduce strict higher level phylogenies where subclades are defined so that the phylogeny is fully resolved from its origin to time xcut, and fully unresolved thereafter, so that for all subclades, stem age > xcut > crown age. We present estimates of speciation and extinction rates from a phylogeny of birds in which this subclade definition was applied. However, for most higher level phylogenies in the literature, it is unclear how higher taxa were defined, but often such phylogenies can be easily transformed into strict higher level phylogenies, as we illustrate by estimating speciation and extinction rates from a near-complete but only partly resolved species-level phylogeny of mammals. The accuracy of our methods is verified using simulations.