The observed parameters of the young super star cluster M82-A1 and its associated compact H II region are here shown to indicate a low heating efficiency or immediate loss, through radiative cooling, of a large fraction of the energy injected by stellar winds and supernovae during the early evolution of the cluster. This implies a bimodal hydrodynamic solution, which leads to a reduced mass deposition rate into the ISM, with a much reduced outflow velocity. We also show here that in order to match the observed parameters of the H II region associated with M82-A1, the resulting star cluster wind should be confined by a high-pressure interstellar medium. The cluster wind parameters, together with the location of the reverse shock, its cooling length, and the radius of the standing outer H II region, are derived analytically. All of these properties are then confirmed with a semianalytical integration of the flow equations, which provides also us with the run of the hydrodynamic variables as a function of radius. The impact of the results is discussed and extended to other massive and young super star clusters surrounded by a compact H II region.