Phylogenetic trees show a remarkable slowdown in the increase of number of lineages towards the present, a phenomenon which cannot be explained by the standard birth-death model of diversification with constant speciation and extinction rates. The birth-death model instead predicts a constant or accelerating increase in the number of lineages, which has been called the pull of the present. The observed slowdown has been attributed to nonconstancy of the speciation and extinction rates due to some form of diversity dependence (i.e., species-level density dependence), but the mechanisms underlying this are still unclear. Here, we propose an alternative explanation based on the simple concept that speciation takes time to complete. We show that this idea of protracted speciation can be incorporated in the standard birth-death model of diversification. The protracted birth-death model predicts a realistic slowdown in the rate of increase of number of lineages in the phylogeny and provides a compelling fit to four bird phylogenies with realistic parameter values. Thus, the effect of recognizing the generally accepted fact that speciation is not an instantaneous event is significant; even if it cannot account for all the observed patterns, it certainly contributes substantially and should therefore be incorporated into future studies.