This work studies joint base station (BS) selection and distributed compression for the uplink of a cloud radio access network. Multiple multi-antenna BSs are connected to a central unit, also referred to as cloud decoder, via capacity-constrained backhaul links. Since the signals received at different BSs are correlated, distributed source coding strategies for communication to the cloud decoder are potentially beneficial. Moreover, reducing the number of active BSs can improve the network energy efficiency, since BS energy consumption provides a major contribution to the overall energy expenditure for the network. An optimization problem is formulated in which compression and BS selection are performed jointly by introducing a sparsity-inducing term into the objective function. An iterative algorithm is proposed. From numerical results, it is observed that the proposed joint BS selection and compression algorithm performs close to the more complex exhaustive search solution.