In-band full-duplex (FD) communications have been optimistically promoted to improve the spectrum utilization and efficiency. However, the penetration of FD communications to the cellular networks domain is challenging due to the imposed uplink/downlink interference. This paper presents a tractable framework, based on stochastic geometry, to study FD communications in cellular networks. Particularly, we assess the FD communications effect on the network performance and quantify the associated gains. The study proves the vulnerability of the uplink to the downlink interference and shows that the improved FD rate gains harvested in the downlink (up to $97\%$) comes at the expense of a significant degradation in the uplink rate (up to $94\%$). Therefore, we propose a novel fine-grained duplexing scheme, denoted as $α$-duplex scheme, which allows a partial overlap between the uplink and the downlink frequency bands. We derive the required conditions to harvest rate gains from the $α$-duplex scheme and show its superiority to both the FD and half-duplex (HD) schemes. In particular, we show that the $α$-duplex scheme provides a simultaneous improvement of $28\%$ for the downlink rate and $56\%$ for the uplink rate. Finally, we show that the amount of the overlap can be optimized based on the network design objective.