A method and arrangement for estimating a DC offset for a signal received in a radio receiver. The received signal includes a digitally modulated signal component, a DC offset component, and a noise component. When the signal is of a known type, such as a Gaussian Minimum Shift Keying (GMSK)-modulated signal with constant amplitude in a GSM/EDGE cellular radio system, the method exploits the known characteristics of the statistical distribution for the known type of signal to obtain a better estimate of the DC offset. The statistical distribution of the received digitally modulated signal component is first analyzed. That statistical distribution is then compared to the known statistical distribution for the known type of signal to identify differences. The differences are then used to estimate the DC offset. Additional iterations may be performed to further improve the DC estimate.