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In this paper, we exploit recent advances in full-duplex (FD) communications and self-interference suppression (SIS) to improve the performance of an opportunistic spectrum access (OSA) system. Specifically, we consider secondary users (SUs) that are equipped with SIS-capable radios. These radios can operate in a simultaneous transmission-and-sensing (TS) mode to improve the detection probability of primary users (PUs), or in a simultaneous transmission-and-reception (TR) mode to enhance the SU throughput. The radios can also revert to the standard sensing-only (SO) mode or perform channel switching (CS). The competing goals of the full-duplex TS and TR modes give rise to a spectrum-awareness/efficiency tradeoff, which can be optimized by allowing the SU link to adaptively switch between various modes, depending on the forecasted PU dynamics. In practice, SIS is imperfect, resulting in residual …