Sensitivity coefficients from Monte Carlo neutron transport codes have uncertainties that can affect nuclear data adjustments with integral experiments. This paper presents an extended version of Generalized Linear Least Squares (GLLS), called xGLLS, that accounts for these uncertainties. With very large sensitivity uncertainties, xGLLS constrains the nuclear data adjustments so that the posterior biases and uncertainties are larger than with GLLS. However, for the range of sensitivity uncertainties realistically encountered, xGLLS does not produce adjustments different from GLLS. This indicates that sensitivity uncertainties are not important compared to experimental, modeling, methodological, and nuclear data uncertainties. To balance a simulation’s accuracy with its computational cost, we recommend stopping a simulation once the uncertainty of a calculated integral parameter, caused by modeling and methodologies and by the sensitivities, is an order of magnitude smaller than that caused by nuclear data.