A method for communication includes producing an error signal by comparing a driving signal applied to a transmitter to an output signal generated by the transmitter in response to the driving signal. The error signal is decomposed into a linear component having a first memory depth and a nonlinear component having one or more polynomial orders and a second memory depth that is less than the first memory depth. First coefficients, up to the first memory depth, of a linear predistortion kernel are computed for application to the driving signal so as to compensate for the linear component of the error signal. Second coefficients for the one or more polynomial orders, up to the second memory depth, of a nonlinear predistortion kernel are computed so as to compensate for the nonlinear component of the error signal. Operation of the transmitter is optimized using the first and second coefficients.