Many cargoes destined for nuclear import carry nuclear localization signals that are recognized by karyopherins (Kaps). We present methods to quantitate import rates and measure Kap and cargo concentrations in single yeast cells in vivo, providing new insights into import kinetics. By systematically manipulating the amounts, types, and affinities of Kaps and cargos, we show that import rates in vivo are simply governed by the concentrations of Kaps and their cargo and the affinity between them. These rates fit to a straightforward pump–leak model for the import process. Unexpectedly, we deduced that the main limiting factor for import is the poor ability of Kaps and cargos to find each other in the cytoplasm in a background of overwhelming nonspecific competition, rather than other more obvious candidates such as the nuclear pore complex and Ran. It is likely that most of every import round is taken up by Kaps and nuclear localization signals sampling other cytoplasmic proteins as they locate each other in the cytoplasm.

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