It is shown that the radio and gamma-ray emission observed from newly-found GeV-bright" supernova remnants (SNRs) can be explained by a model, in which a shocked cloud and shock-accelerated cosmic rays (CRs) frozen in it are simultaneously compressed by the supernova blastwave as a result of formation of a radiative cloud shock. Simple reacceleration of pre-existing CRs is generally sufficient to power the observed gamma-ray emission through the decays of 0-mesons produced in hadronic interactions between high-energy protons (nuclei) and gas in the compressed-cloud layer. This model provides a natural account of the observed synchrotron radiation in SNRs W51C, W44 and IC 443 with flat radio spectral index, which can be ascribed to a combination of secondary and reaccelerated electrons and positrons. Show Partial Abstract