Extending the Froehlich polaron problem to a discrete ionic lattice we study a polaronic state with a small radius of the wave function but a large size of the lattice distortion. We calculate the energy dispersion and the effective mass of the polaron with the 1/lambda perturbation theory and with the exact Monte Carlo method in the nonadiabatic and adiabatic regimes, respectively. The ``small Froehlich polaron is found to be lighter than the small Holstein polaron by one or more orders of magnitude.
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