The "mental rotation" literature has studied how subjects determine whether two stimuli that differ in orientation have the same handedness. This literature implies that subjects perform the task by imagining the rotation of one of the stimuli to the orientation of the other. This literature has spawned several theories of mental representation. These theories imply that mental representations cannot be both orientation-free and handedness-specific. We present four experiments that demonstrate the contrary: mental representations can be both orientation-free and handedness-specific. In Experiment 1 we serendipitously discovered a version of R. N. Shepard and J. Metzler's (1971) "mental rotation" task in which subjects accurately discover the handedness of a stimulus without using "mental rotation," i.e., in which reaction time to compare the handedness of two forms is not a function of the angular disparity between the two forms. In Experiment 2 we generalize this finding to different experimental procedures. In Experiment 3 we replicate this finding with a much larger group of subjects. In Experiment 4 we show that when we preclude the formation of an orientation-free representation by never repeating a polygon, subjects carry out the handedness comparison task by performing "mental rotation."