Conventional research on energy-efficient wireless systems tends to focus on saving transmit energy. However, as the evolution of wireless systems moves towards shorter distance transmission and smaller cell sizes, the computational energy in wireless hardware becomes significant alongside transmit radio energy. In this paper, we develop energy models for a point-to-point wireless transmission that consider practical aspects such as multipath fading, error-control coding and receiver synchronization. The total energy consumption of the wireless system is modeled as a function of modulation scheme, data rate, signal bandwidth, code rate, received signal-to-noise ratio (SNR) and channel parameters. We choose a multipath Rayleigh-fading channel model and Reed-Solomon coding scheme for the numerical analyses. Simulation results show that there exists an optimal parameter configuration that gives the minimum energy consumption for given data and bit-error rates. At short transmission distances, computational energy dominates and higher-order modulation schemes with low bandwidth allocation are shown to be more energy efficient.