A transmitter clips a transmission signal before transmission in order to reduce the strength of at least one peak of the transmission signal exceeding a predetermined threshold. The transmitter includes a clipper having a minimizer, a filter and an adder. The minimizer minimizes of a cost function with respect to an optimization signal, the cost function having weighted terms as a function of the optimization signal. The terms relate to an effective modulation distortion and an effective overshoot exceeding the predetermined threshold. The filter forms a clipping signal by filtering the optimization signal formed as a result of the minimization according to the spectrum emission mask requirements of the radio system. The adder subtracts the clipping signal from the transmission signal.