This work introduces an imaging device that efficiently captures spectral images along with a mathematical model that allows reconstructs them from far fewer measurements than those required by conventional scanning devices. This imaging architecture captures multiplexed representations of the multidimensional information by placing an electrostatic membrane mirror into the optical train of a compressive snapshot imager that employs a color-mosaic attached to the detector. Results show that a gain up to 5 dB of the peak-signal-to-noise ratio is achieved in contrast to a traditional multishot compressive spectral system that requires mechanical displacement of its optical elements.