Motivated by the increasing interest in energy-efficient communication systems, the relation between energy efficiency (EE) and spectral efficiency (SE) for multiple-input-multiple-output (MIMO) systems is investigated in this paper. To provide insights into the design of practical MIMO systems, we adopt a realistic power model and consider both independent Rayleigh fading and semicorrelated fading channels. We derived a novel and closed-form upper bound (UB) for the system EE as a function of SE. This UB exhibits great accuracy for a wide range of SE values and, thus, can be utilized for explicit assessment of the influence of SE on EE and for analytically addressing the EE optimization problems. Using this tight EE UB, our analysis unfolds two EE optimization issues: Given the number of transmit and receive antennas, an optimum value of SE is derived, such that the overall EE can be maximized, and given a specific value of SE, the optimal number of antennas is derived for maximizing the system EE.