Distributed spectrum sensing enhances the detection reliability of a cognitive radio network. However, this comes at the price of a higher energy consumption. To solve this problem, a combined censoring and sleeping scheme is considered where the cognitive radios switch off their sensing module with a specific sleeping rate in each sensing period. The awake cognitive radios send their local decisions to the fusion center only if it is deemed to be informative. The fusion center either employs the OR or the AND rule to make the final decision about the presence or absence of the primary user. This paper investigates which rule performs better in terms of energy efficiency under various conditions. The underlying sensing parameters are derived by minimizing the maximum average energy consumption per sensor subject to a constraint on the probabilities of false alarm and detection. This way, it can be ensured that the spectrum opportunities are utilized efficiently while the primary users are not interfered with. A case study based on IEEE 802.15.4/ZigBee is considered for performance evaluation. It is shown that significant energy savings can be obtained by employing combined censoring and sleeping.