The magnetotelluric method is increasingly being used to monitor electrical resistivity changes in the subsurface. One of the preferred parameters derived from the surface impedance is the strike direction, which is very sensitive to changes in the direction of the subsurface electrical current flow. The preferred method for estimating the strike changes is that provided by the phase tensor because it is immune to galvanic distortions. However, it is also a fact that the associated analytic formula is unstable for noisy data, something that limits its applicability for monitoring purposes, because in general this involves comparison of two or more very similar data sets. On the other hand, the classical Swift’s approach for strike is very stable for noisy data but it is severely affected by galvanic distortions. In this paper we impose the criterion of Swift’s approach to the phase tensor. Rather than developing an analytical formula we optimize numerically the same criterion. This stabilizes the estimation of strike by relaxing an exact condition to an optimal condition in the presence of noise. This has the added benefit that it can be applied to windows of several periods, thus providing tradeoffs between variance and resolution. The performance of the proposed approach is illustrated by its application to synthetic data and to real data from a monitoring array in the Cerro Prieto geothermal field, México.