The Michelson interferometer is one of the best established tools for quantitative interferometric measurements. It has been, and is still successfully used, not only for scientific purposes, but it is also introduced in undergraduate courses for qualitative demonstrations as well as for quantitative determination of several properties such as refractive index, wavelength, optical thickness, etc. Generally speaking, most of the measurements are carried out by determining phase distortions through the changes in the location and/or shape of the interference fringes. However, the extreme sensitivity of this tool, for which minimum deviations of the conditions of its branches can cause very large modifications in the fringe pattern, makes phase changes difficult to follow and measure. The purpose of this communication is to show that, under certain conditions, the sensitivity of the Michelson interferometer can be "turned down" allowing the quantitative measurement of phase changes with relative ease. As an example we present how the angle (or, optionally, the refractive index) of a transparent standard optical wedge can be determined. Experimental results are shown and compared with the data provided by the manufacturer showing very good agreement. (Contains 5 figures.)