A MEMS device includes a bottom plate structure supporting a conductive electrode. A flexible conductive top plate movably supported by a flexure is affixed to a small peripheral portion of the top plate that is aligned with the electrode. Drive circuitry applies a high level of a drive voltage signal between the electrode and the top plate to produce an attracting electrostatic force between the top plate and the electrode sufficient to overcome the flexure and draw the top plate against the electrode. The drive circuitry later applies a low level of the drive voltage signal to remove the electrostatic force and allow the flexure to peel the peripheral portion away from the electrode. Additional drive voltage signals may be applied to additional electrodes to draw additional peripheral portions of the top plate against the additional electrodes and successively removed to allow peripheral portions of the top plate to be sequentially peeled away from the electrodes.