In-band full-duplex (FD) communications have been optimistically promoted to improve the spectrum utilization in cellular networks. However, the explicit impact of spatial interference, imposed by FD communications, on uplink and downlink transmissions has been overlooked in the literature. This paper presents an extensive study of the explicit effect of FD communications on the uplink and downlink performances. For the sake of rigorous analysis, we develop a tractable framework based on stochastic geometry toolset. The developed model accounts for uplink truncated channel inversion power control in FD cellular networks. The study shows that FD communications improve the downlink throughput at the expense of significant degradation in the uplink throughput. Therefore, we propose a novel fine-grained duplexing scheme, denoted as α-duplex scheme, which allows a partial overlap between uplink and downlink frequency bands. To this end, we show that the amount of the overlap can be optimized via adjusting α to achieve a certain design objective.