In compressional optical coherence elastography, phase-variation gradients are used for estimating quasistatic strains created in tissue. Using reference and deformed optical coherence tomography (OCT) scans, one typically compares phases from pixels with the same coordinates in both scans. Usually, this limits the allowable strains to fairly small values to , with the caveat that such weak phase gradients may become corrupted by stronger measurement noises. Here, we extend the OCT phase-resolved elastographic methodology by (1) showing that an order of magnitude greater strains can significantly increase the accuracy of derived phase-gradient differences, while also avoiding error-phone phase-unwrapping procedures and minimizing the influence of decorrelation noise caused by suprapixel displacements, (2) discussing the appearance of artifactual stiff inclusions in resultant OCT elastograms in the vicinity of bright scatterers due to the amplitude-phase interplay in phase-variation measurements, and (3) deriving/evaluating methods of phase-gradient estimation that can outperform conventionally used least-square gradient fitting. We present analytical arguments, numerical simulations, and experimental examples to demonstrate the advantages of the proposed optimized phase-variation methodology.