Variations in polarization efficiency (p/A) of interstellar grains as a function of environment place vital constraints on models for the mechanism of their alignment. We use polarimetry of background field stars to investigate alignment in the Taurus dark cloud as a function of optical depth for extinctions of A_K < 2.5 (A_V < 25). Results show a strong systematic trend in polarization efficiency with extinction. We discuss the possibility of a relationship between p/A and icy grain mantle growth, since mantles are detected in Taurus only for extinctions where p/A is lowest. A simple density model of alignment by paramagnetic alignment (Davis & Greenstein 1951) predicts that the magnetic field strength (B) scales with density to the power k=0.28.