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Due to the rise of the energy efficiency (EE) as a system performance evaluation criterion, the EE-spectral efficiency (SE) trade-off is becoming a key tool for getting insight on how to efficiently design future communication system. As far as the single-input single-output (SISO) Rayleigh fading channel is concerned, the EE-SE trade-off has been accurately approximated in the past but only at low-SE. In this paper, we propose a novel and more generic closed-form approximation (CFA) of this EE-SE trade-off which is very accurate for any SE values. We compare our CFA with two existing CFAs and show the great accuracy of the former for a wider range of SE in comparison with the latter. As an application, we use our CFA to study the variation of EE-SE trade-off when a realistic power model is assumed and to compare the energy consumption of SISO against a 2×2 multi-input multi-output (MIMO) system over the Rayleigh fading channel.