Rotary motors of bacterial flagella are driven by ions that move across the cytoplasmic membrane down an electrochemical gradient. For Escherichia coli, the ions are protons, and the maximum work per unit charge that they can do is the protonmotive force. To test whether motor efficiency is limited by proton leakage or mechanical nonlinearities, we measured torque as a function of protonmotive force. Filamentous cells were drawn into micropipettes and energized with an external voltage source. Torque was proportional to protonmotive force up to -150 mV, twice the span accessible by earlier techniques. This is consistent with a mechanism in which a fixed number of protons, working at unit efficiency, carry the motor through each revolution. We also found that individual torque-generating elements inactivate at low potentials or potentials of reverse sign. When normal potentials are restored, they reactivate sequentially.