We propose a cognitive radio system in fading environments where the secondary sender opportunistically violates the secondary-to-primary (S-P) interference power limit. Assuming a slowly-varying fading interference channel with two-senders and two-receivers, the primary sender adjusts its rate and power depending on its own channel, while ignoring the secondary user. Through an optimization process, the secondary sender's rate and power are determined and the decision is made on whether the secondary sender violates the S-P interference power limit. The primary receiver removes the effect of excessive S-P interference by multiuser decoding (MUD) which jointly decodes the primary and secondary senders' data. Achievable rates of the proposed system are examined by computer simulation. It was observed that the proposed system tends to violate the SP interference power limit when the S-P channel gain is larger than the other channel gains. Remarkably, the proposed system can provide a considerably high data rate for the secondary user even without sacrificing the data rate for the primary user over a wide range of signal-to-noise ratios.