Iterative least square phase-measuring techniques address the phase-shifting interferometry issue of sensitivity to vibrations and scanner nonlinearity. In these techniques the wavefront phase and phase steps are determined simultaneously from a single set of phase-shifted fringe frames where the phase shift does not need to have a nominal value or be a priori precisely known. This method is commonly used in laser interferometers in which the contrast of fringes is constant between frames and across the field. We present step-by-step modifications to the basic iterative least square method. These modifications allow for vibration insensitive measurements in an interferometric system in which fringe contrast varies across a single frame, as well as from frame to frame, due to the limited bandwidth light source and the nonzero numerical aperture of the objective. We demonstrate the efficiency of the new algorithm with experimental data, and we analyze theoretically the degree of contrast variation that this new algorithm can tolerate.