The increase in cloud optical depth with warming at middle and high latitudes is a robust cloud feedback response found across all climate models. This study builds on results that suggest the optical depth response to temperature is timescale invariant for low-level clouds. The timescale invariance allows one to use satellite observations to constrain the models' optical depth feedbacks. Three passive-sensor satellite retrievals are compared against simulations from eight models from the Atmosphere Model Intercomparison Project (AMIP) of the 5th Coupled Model Intercomparison Project (CMIP5). This study confirms that the low-cloud optical depth response is timescale invariant in the AMIP simulations, generally at latitudes higher than 40°. Compared to satellite estimates, most models overestimate the increase in optical depth with warming at the monthly and interannual timescales. Many models also do not capture the increase in optical depth with estimated inversion strength that is found in all three satellite observations and in previous studies. The discrepancy between models and satellites exists in both hemispheres and in most months of the year. A simple replacement of the models' optical depth sensitivities with the satellites' sensitivities reduces the negative shortwave cloud feedback by at least 50% in the 40°–70°S latitude band and by at least 65% in the 40°–70°N latitude band. Based on this analysis of satellite observations, we conclude that the low-cloud optical depth feedback at middle and high latitudes is likely too negative in climate models.