There is presented mechanisms for handling input envelope representation coefficients. A method is performed by an encoder of a communication system. The method comprises determining envelope representation residual coefficients as first compressed envelope representation coefficients subtracted from the input envelope representation coefficients. The method comprises transforming the envelope representation residual coefficients into a warped domain so as to obtain transformed envelope representation residual coefficients. The method comprises applying, at least one of a plurality of gain-shape coding schemes on the transformed envelope representation residual coefficients in order to achieve gain-shape coded envelope representation residual coefficients, where the plurality of gain-shape coding schemes have mutually different trade-offs in one or more of gain resolution and shape resolution for one or more of the transformed envelope representation residual coefficients. The method comprises transmitting, over a communication channel to a decoder, a representation of the first compressed envelope representation coefficients, the gain-shape coded envelope representation residual coefficients, and information on the at least one applied gain-shape coding scheme.