The substantial increase in the number of base stations (BSs) compels researchers to focus on spectral efficiency (SE) and energy efficiency (EE) in wireless networks. To this end, we propose an intracell frequency band exiling (ICE) technique as a promising solution for green wireless networks. In the proposed technique, operating frequency bands of mobile users are assigned from upper frequency bands (UFBs) to lower frequency bands (LFBs) by suitably adjusting their coverage area to provide energy-efficient communications. To do this, we derive ICE probabilities on a log-normally distributed traffic model and calculate the EE and area SE (ASE) considering the power consumption model. The simulation results demonstrate that the ASE can be improved by increasing the traffic density. However, increasing the traffic density does not improve the EE beyond a certain threshold. Therefore, we present the tradeoff between EE and ASE and provide an optimum operating point. In addition, we show the ICE performance to be better than that of the existing cell-zooming (CZ) technique, unveil the ICE relation with beyond-5G (B5G) networks, and, finally, provide a cell-exiling manager system to illustrate the applicability of the proposed technique for various implementations.