Predicting the peak amplitude of the sunspot cycle is a key goal of solar-terrestrial physics. The precursor method currently favored for such predictions is based on the dynamo model in which large-scale polar fields on the decline of the 11-year solar cycle are converted to toroidal (sunspot) fields during the subsequent cycle. The strength of the polar fields during the decay of one cycle is assumed to be an indicator of peak sunspot activity for the following cycle. Polar fields reach their peak amplitude several years after sunspot maximum; the time of peak strength is signaled by the onset of a strong annual modulation of polar fields due to the 7$^{1}\!big/\!_{4}$¿ tilt of the solar equator to the ecliptic plane. Using direct polar field measurements, now available for four solar cycles, we predict that the approaching solar cycle 24 (~2011 maximum) will have a peak smoothed monthly sunspot number of 75 ¿ 8, making it potentially the smallest cycle in the last 100 years.