Passive microwave satellite observations of ice extent and concentration form the foundation of sea ice model evaluations, due to their wide spatial coverage and decades-long availability. Observations related to other model quantities are somewhat more limited but increasing as interest in high-latitude processes intensifies. Sea ice thickness, long judged a critical quantity in the physical system, is now being scrutinized more closely in sea ice model simulations as more expansive measurements become available. While albedo is often the first parameter chosen by modelers to adjust simulated ice thickness, this paper explores a set of less prominent parameters to which thickness is also quite sensitive. These include parameters associated with sea ice conductivity, mechanical redistribution, oceanic heat flux, and ice–ocean dynamic stress, in addition to shortwave radiation. Multiple combinations of parameter values can produce the same mean ice thickness using the Los Alamos Sea Ice Model, CICE. One of these “tuned” simulations is compared with a variety of observational data sets in both hemispheres. While deformed ice area compares well with the limited observations available for ridged ice, thickness measurements differ such that the model cannot agree with all of them simultaneously. Albedo and ice–ocean dynamic parameters that affect the turning of the ice relative to the ocean currents have the largest effect on ice thickness, of the parameters tested here. That is, sea ice thickness is highly sensitive to changes in external forcing by the atmosphere or ocean, and therefore serves as a sensitive diagnostic for high-latitude change.