Cognitive radios process their sensed information collectively in order to opportunistically identify and access underutilized spectrum segments (spectrum holes). Due to the transient and rapidly varying nature of the spectrum occupancy, the cognitive radios (secondary users) must be agile in identifying the spectrum holes in order to enhance their spectral efficiency. We propose a novel adaptive procedure to reinforce the agility of the secondary users for identifying multiple spectrum holes simultaneously over a wide spectrum band. This is accomplished by successively exploring the set of potential spectrum holes and progressively allocating the sensing resources to the most promising areas of the spectrum. Such exploration and resource allocation results in conservative spending of the sensing resources and translates into very agile spectrum monitoring. The proposed successive and adaptive sensing procedure is in contrast to the more conventional approaches that distribute the sampling resources equally over the entire spectrum. Besides improved agility, the adaptive procedure requires less-stringent constraints on the power of the primary users to guarantee that they remain distinguishable from the environment noise and renders more reliable spectrum hole detection.