Doping--the intentional introduction of impurities into a material--is fundamental to controlling the properties of bulk semiconductors. This has stimulated similar efforts to dope semiconductor nanocrystals. Despite some successes, many of these efforts have failed, for reasons that remain unclear. For example, Mn can be incorporated into nanocrystals of CdS and ZnSe (refs 7-9), but not into CdSe (ref. 12)--despite comparable bulk solubilities of near 50 per cent. These difficulties, which have hindered development of new nanocrystalline materials, are often attributed to 'self-purification', an allegedly intrinsic mechanism whereby impurities are expelled. Here we show instead that the underlying mechanism that controls doping is the initial adsorption of impurities on the nanocrystal surface during growth. We find that adsorption--and therefore doping efficiency--is determined by three main factors: surface morphology, nanocrystal shape, and surfactants in the growth solution. Calculated Mn adsorption energies and equilibrium shapes for several nanocrystals lead to specific doping predictions. These are confirmed by measuring how the Mn concentration in ZnSe varies with nanocrystal size and shape. Finally, we use our predictions to incorporate Mn into previously undopable CdSe nanocrystals. This success establishes that earlier difficulties with doping are not intrinsic, and suggests that a variety of doped nanocrystals--for applications from solar cells to spintronics--can be anticipated.