Cooperative spectrum sensing among multiple cognitive radios mitigates the effects of shadowing and fading. However, it also generates overhead traffic which consumes more power in battery operated mobile terminals. In this paper a censoring scheme for spectrum sensing is proposed. Only informative test statistics are transmitted to the fusion center or shared with other secondary users. Two cooperative censoring test statistics based on cyclostationarity are proposed. Constant false alarm rate tests are derived and asymptotic distributions of test statistics established. The asymptotic distributions are approximated using characteristic functions. Limits for the censoring (no-send) region are derived. The performance of the proposed censoring scheme is illustrated through simulations in a multipath radio environment. Only a minor performance loss is experienced in comparison to uncensored cooperative detection even under very strict constaints on communication rates for the secondary users.