This work investigates the joint design of fronthaul compression and precoding for the downlink of Cloud Radio Access Networks (C-RANs). The main goal is that of bringing insight into an aspect of the optimal functional split between Radio Units (RUs) and Central Unit (CU), namely: where should precoding be performed? Unlike previous works, we tackle this issue for a practical scenario with block-ergodic channels and either instantaneous or stochastic Channel State Information (CSI) at the CU. Optimization algorithms over fronthaul compression and precoding are proposed that are based on a stochastic successive upper-bound minimization approach. Via numerical results, the relative merits of two strategies, in which precoding is carried out at the CU or at the RUs, are evaluated as a function of system parameters such as fronthaul capacity and channel coherence time under either instantaneous or stochastic CSI at the CU.