A previously derived asymptotic expression for the reflection coefficient at the feed of a paraboloidal reflector antenna covered with a paraboloidal radome is shown to be valid, with suitable modifications, for general reflector-radome configurations. This generalisation is illustrated through the particular choice of a paraboloidal reflector covered with a spherical radome. The generalised asymptotic expression for this geometry agrees very well with the numerically calculated integral expression obtained by the power coupling theorem.