We measured the masking of a spatial 4-cycle/deg sinusoid in the presence of both random and sinusoidal masks. Subjects used a variety of detection strategies, depending on psychophysical technique and familiarity with the mask. Some strategies produce Weber's-law behavior and appear formally equivalent to identification tasks; we hypothesize that these exemplify the operation of Birdsall's theorem. Other strategies produce power-law behavior and are more like the simpler detection task. Our results suggest that criterion change (commonly uncontrolled in masking studies) can produce an unacceptably large bias in the results.