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The momentum averaging (MA) approach to the evaluation of the single-electron Green's Function (GF) was proposed in a recent Letter, as a new and accurate approximation for the Holstein polaron problem. Indeed, in the range of parameter s considered in the Letter, the MA approximation accurately reproduces the investigated polaron properties. However, as shown here, the applicability of this approximation is restricted by two fundamental limitations. The MA contributions to the inco herent continuum are greatly oversimplified. Similarly, the adiabatic correlations described by phonons appearing simultaneou sly at different lattice sites are entirely ignored.