In this paper, we describe a method that allows one to realize highly efficient amplitude modulation of radiation at the output of electro-optical laser switches with two coupled resonators, in which electro-optical elements are located both in two split arms and in every arm of a multipath interferometer with combined channels with a control voltage 2 times lower than in existing laser switches. Moreover, the electro-optical elements located in the two split arms of a multipath interferometer with combined channels, with one passage of the light flux through the electro-optical element, must make the opposite controlled changes in the phase difference of the interfering light beams. Therefore, for such electro-optical switches with two coupled resonators the value of the required electric power will be, respectively, 2 times less than that of the existing ones, which significantly expands their operating frequency range. In this case, a laser switch with electrooptical elements located in the two split arms of a multipath interferometer has an asymmetric dependence of the output radiation intensity on the change in the phase difference of the interfering light beams relative to the zero value of the light intensity. A laser switch with electro-optical elements located on all arms of a multipath interferometer with combined channels has a symmetric dependence of the output radiation intensity on the magnitude of the phase difference of the interfering light beams relative to the zero value of the light intensity. In addition, due to the coherent summation of the amplitudes of the interfering light waves, such laser electro-optical shutters also have amplification of radiation with a resonant wavelength.