Typical equilibrium reconstructions for axisymmetric plasma confinement devices involve a nonlinear least squares minimization with respect to parameters of the Grad–Shafranov equation. These parameters specify the toroidal field and pressure as functions of the poloidal flux, and the fit minimizes a cost function, χ2, which involves measurements such as the tangential poloidal field near the boundary. Most fitting procedures in use weigh the terms in χ2 by the variances of the measurements, but none accounts for the possibility of correlations between the measurements. Results presented here indicate that the presence of correlations may have a strong effect on the fidelity of the fit, possibly beneficial when they are optimally accounted for but quite detrimental otherwise. These results also show that increasing the number of measurements of the same type can have little effect when the additional measurements are within a correlation scale length of the previous measurements. A further issue is that the toroidal field and pressure terms in the Grad–Shafranov equation play nearly the same role, leading to a near-degeneracy in the fit. Internal pressure measurements most effectively mitigate this near-degeneracy when correlations are optimally treated.