In this contribution we present new achievable rates, for the non-fading uplink channel of a cellular network, with joint cell-site processing, where unlike previous results, the error-free backhaul network has finite capacity per-cell. Namely, the cell-sites are linked to the central joint processor via lossless links with finite capacity. The cellular network is modeled by the circular Wyner model, which yields closed form expressions for the achievable rates. For this idealistic model, we present achievable rates for cell-sites that use compress-and forward scheme, combined with local decoding, and inter-cell time-sharing. These rates are then demonstrated to be rather close to the optimal unlimited backhaul joint processing rates, already for modest backhaul capacities, supporting the potential gain offered by the joint cell-site processing approach.