Full-field measurements are used to calibrate material parameters. The Equilibrium Gap Method (EGM), like other identification formulations that use full-field data, has the advantage of being direct for linear behavior and some nonlinearities, thereby being computationally cheaper than iterative methods. However, it has a high sensitivity to measurement uncertainties, which is detrimental when dealing with noisy data. The Reconditioned Equilibrium Gap Method (REGM) has been proposed to mitigate this sensitivity. Reconditioning is revisited in this paper from two viewpoints. First, reconditioning may be analyzed as a way of accounting for displacement uncertainties in the cost function. Second, the reconditioned formulation approximates the optimization problem associated with Finite Element Model Updating (FEMU). Based on these developments, the Sequentially Reconditioned Equilibrium Gap Method (SREGM), i.e., an intermediary between FEMU and REGM, is proposed. It uses REGM results to correct the approximation in a fixed-point scheme. Identification results on synthetic and true experiments show that considering the covariance matrix of measured displacements in the cost function is necessary to obtain good identification results. The analyses give insight into unsuccessful cases and confirm that SREGM provides results closer to FEMU than EGM or REGM.