Program instructions that consume and produce small operands can be executed in hardware circuitry of less than full size. We compare different proposed models of accounting for the usefulness of bit-positions in operands, using a run-time profiling tool, both to observe and summarize operand values, and to reconstruct and analyze the program’s data-flow graph to discover useless bits. We find that under aggressive models, the average number of useful bits per integer operand is as low as 10, not only in kernels but also in general-purpose applications from SPEC95.