Vast segments of the frequency spectrum are licensed to specific users for particular applications. These legacy users, however, often under-utilize their designated spectrum segments. Unlicensed (secondary) users can benefit from this fact and opportunistically exploit the vacant spectrum segments (spectral holes). Due to the transient nature of the spectrum occupancy it becomes imperative for secondary users to quickly identify such spectral holes. To accomplish this, we propose a novel sequential and adaptive spectrum sensing procedure. The underlying notion of this procedure is to progressively allocate the sensing resources to only the most promising areas of the spectrum. This translates in a reduction of sensing resources and time needed to accurately identify spectrum holes, in contrast with more conventional approaches that allocate the sensing budget over the entire spectrum uniformly. The proposed method is theoretically sound and further supported by simulation results.