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Cognitive Radio (CR) is a new concept in wireless communication systems that aims at enabling dynamic access to the frequency spectrum for unlicensed secondary users (SU) through the reuse of licensed frequencies. Specifically, CR systems are expected to detect idle frequency bands that are not actively used by licensed primary users (PU) by applying a spectrum sensing procedure, to take advantage of them for providing service to SU, and to release them to the PU upon request. The duration of the spectrum sensing procedure is an overhead factor that affects the actual utilization of the spectrum by the CR system, and in this paper we propose a new method for adapting the duration of energy-based spectrum sensing window that improves the detection of PU signals as well as the utilization of spectrum opportunities. We present also numerical results obtained from simulations which confirm the effectiveness of the proposed method.