Energy efficiency has become increasingly important in wireless communications nowadays. Saving energy will not only reduce operating cost but also reduces greenhouse gas emissions, which is important for combating climate change. The authors propose energy-efficient user grouping algorithms to provide power minimisation of grouped multi-carrier code division multiple access (MC-CDMA) and space-time block coding MC-CDMA systems in a cellular environment. Depending on the channel fading conditions, power control is utilised to minimise the total transmitted power under a bit error rate constraint. When the allocation is performed without a fair data rate requirement, the authors provide the optimal solution to the minimisation problem. However, when some fairness is considered, the optimal solution requires high computational complexity. Thus, the authors solve the problem by proposing two suboptimal algorithms. Simulation results illustrate a significantly reduced power consumption in comparison with other techniques.