We consider the motion of electrons in the electromagnetic field structure which is typical for the ramp of the quasi-perpendicular collisionless shock. The total energy that an electron can gain due to the crossing of the stationary shock front is determined by the cross-shock potential in the de Hoffman-Teller frame. When the shock is wide the electrons are accelerated by the electric field along the magnetic field, while the perpendicular energy gain is adiabatic v2⊥∝B. If, however, the ramp is narrow enough, the electrons are effectively demagnetized, and a considerable fraction of the cross-shock potential energy can be transferred directly into the electron perpendicular energy, causing substantial overadiabatic energization. This effect may be closely related to the strong heating of electrons in the supercritical shocks. ¿ American Geophysical Union 1995