We develop and test two functional hypotheses based on the sampling theory of visual resolution that might account for letter acuity in peripheral vision. First, a letter smaller than the acuity limit provides insufficient veridical energy for performing the task, and, second, the available veridical energy is masked by increased amounts of visible but aliased energy. These two hypotheses make opposite predictions about the effect of low-pass filtering on letter acuity, which we tested experimentally by using filtered letters from the tumbling-E alphabet. Our results reject the masking hypothesis in favor of the energy insufficiency hypothesis. Additional experiments in which high-pass-filtered letters were used permitted the isolation of a critical band of spatial frequencies, which is necessary and sufficient for achieving maximum visual acuity. This critical band varied with the particular pair of letters to be discriminated but was in the range 0.9-2.2 cycles per letter.