Nuclear localization signals (NLSs) target proteins into the nucleus through mediating interactions with nuclear import receptors. Here, we perform a quantitative analysis of the correlation between NLS receptor affinity and the steady-state distribution of NLS-bearing cargo proteins between the cytoplasm and the nucleus of live yeast, which reflects the relative import rates of various NLS sequences. We find that there is a complicated, but monotonic quantitative relationship between the affinity of an NLS for the import receptor, importin alpha, and the steady-state accumulation of the cargo in the nucleus. This analysis takes into consideration the impact of protein size. In addition, the hypothetical upper limit to an NLS affinity for the receptors is explored through genetic approaches. Overall, our results indicate that there is a correlation between the binding affinity of an NLS cargo for the NLS receptor, importin alpha, and the import rate for this cargo. This correlation, however, is not maintained for cargoes that bind to the NLS receptor with very weak or very strong affinity.