It is shown that electrons with momenta exceeding the `free electron limit of $m_eca_0^2/2$ can be produced when a laser pulse and a longitudinal electric field interact with an electron via a non-wakefield mechanism. The mechanism consists of two stages: the reduction of the electron dephasing rate $gamma-p_x/m_ec$ by an accelerating region of electric field and electron acceleration by the laser via the Lorentz force. This mechanism can, in principle, produce electrons that have longtudinal momenta that is a significant multiple of $m_eca_0^2/2$. 2D PIC simulations of a relatively simple laser-plasma interaction indicate that the generation of super-ponderomotive electrons is strongly affected by this `anti-dephasing mechanism.
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