The observed modulation of the period and amplitude of Polaris, the short-period classical Cepheid, may be cyclical, though irregular, and superimposed on the continuing evolutionary changes of this star. If so, it curiously resembles the Blazhko effect seen in RR Lyrae stars, as Evans and her colleagues have noted. The present author's recent theory of the Blazhko effect based on a solar-like magnetoconvective cycle in the stellar envelope is here applied to Polaris, with some limited success. The theory may also explain the slow cycle seen in another shortperiod Cepheid, V473 Lyr. It is therefore possible to predict, tentatively, an entire new class of short-period "Blazhko Cepheids."