Kinesin is a dimeric motor with twin catalytic heads joined to a common stalk. Kinesin molecules move processively along microtubules in a hand-over-hand walk, with the two heads advancing alternately. Recombinant kinesin constructs with short stalks have been found to "limp", i.e., exhibit alternation in the dwell times of successive steps. Limping behavior implies that the molecular rearrangements underlying even- and odd-numbered steps must differ, but the mechanism by which such rearrangements lead to limping remains unsolved. Here, we used an optical force clamp to measure individual, recombinant dimers and test candidate explanations for limping. Introducing a covalent cross-link into the stalk region near the heads had no effect on limping, ruling out possible stalk misregistration during coiled-coil formation as a cause. Limping was equally unaffected by mutations that produced 50-fold changes in stalk stiffness, ruling out models where limping arises from an asymmetry in torsional strain. However, limping was enhanced by perturbations that increased the vertical component of load on the motor, including increases in bead size or net load, and decreases in the stalk length. These results suggest that kinesin heads take different vertical trajectories during alternate steps, and that the rates for these motions are differentially sensitive to load.