A method and apparatus in a radio receiver for canceling interference from a high power, high data rate signal received in a combined signal that includes a contribution from the high power signal and a contribution from a lower power signal. It is first determined whether the high power signal was correctly received. A CRC checksum may be used to determine whether the high power signal was received with a good reliability. Thereafter, the contribution of the high power signal is removed from the received signal only if the high power signal was correctly received. The contribution of the high power signal may be removed by hard-subtracting the contribution of the high power signal from the received signal if all of the bits of the checksum are correct, and soft-subtracting the contribution of the high power signal from the received signal if most, but not all, of the bits in the checksum are correct.