The efficiency with which spectrum is used in wireless communications systems is becoming increasingly important as a result of the expected growth in traffic demand and the finite nature of usable spectrum. Spectral efficiency, defined as throughput divided by bandwidth, is a useful metric for evaluating the use of spectrum in wireless systems. In any given area the achievable spectrum efficiency is impacted by the underlying user population. This paper presents the methodology for finding the transmit power which maximises the spectral efficiency of a LTE cell for a given user density and traffic type. The impact of different user densities and traffic profiles on the choice of transmit power is evaluated. Results show that the transmit power which maximise spectral efficiency decreases as the user density and average data rate of the traffic profile increases. Two non ideal real world scenarios which require an increase in cell spectral efficiency are also considered and a modified user admission scheme which can increase the cell spectral efficiency is presented and evaluated. Results showed that the spectral efficiency was improved but the maximum improvement depended on the traffic profile and practical constraints of the LTE standard.