Apparatus (18) for performing a medical procedure on a beating heart (20) includes a mechanical stabilization element (25), a surface (27) of which is adapted to be applied to a segment (24) of the heart to reduce motion of the segment. One or more electrodes (100) are fixed to the surface of the stabilization element, so as to contact the segment when the stabilization element is applied to the segment. Preferably, at least one of the one or more electrodes is adapted to apply electrical signals to the segment so as to further reduce motion thereof, while the heart continues to pump blood.