We discuss the use of regression diagnostics combined with nonlinear least-squares to refine cell parameters from powder diffraction data, presenting a method which minimizes residuals in the experimentally-determined quantity (usually 2θ_hkl or energy, E_hkl). Regression diagnostics, particularly deletion diagnostics, are invaluable in detection of outliers and influential data which could be deleterious to the regressed results. The usual practice of simple inspection of calculated residuals alone often fails to detect the seriously deleterious outliers in a dataset, because bare residuals provide no information on the leverage (sensitivity) of the datum concerned. The regression diagnostics which predict the change expected in each cell constant upon deletion of each observation (hkl reflection) are particularly valuable in assessing the sensitivity of the calculated results to individual reflections. A new computer program, implementing nonlinear regression methods and providing the diagnostic output, is described.