Constant load measurements by nanoindentation offer the potential for measuring strain rate sensitivity from individual features and defects on a submicron scale. However, recent reports reveal a conflicting load dependence (both increasing and decreasing strain rate sensitivity with load) which has yet to be fully explained. In this study, constant load measurements on five materials (Zn, Al, Cu, Ti, and SiO2) were conducted over a range of peak loads, and then compared with both constant strain rate results and conventional values in the literature. The load dependence was found to be caused by the increasing contribution of drift errors throughout the test. A proposed framework, involving higher loads, shorter hold and loading times, and a physically sound fitting method, was found to produce unambiguous results free from load dependencies, with improved correlations to conventional values and reduced standard deviations.