Over the past years, multimedia communication technologies have demanded higher computing power availability and, therefore, higher energy consumption. In order to meet the challenge to provide software-based video encoding solutions with reduced consumption, we adopted a software implementation of a state-of-the-art video encoding standard and optimized its implementation in the energy (E) sense. Thus, besides looking for the coding options which lead to the best fidelity in a rate-distortion (RD) sense, we constrain the video encoding process to fit within a certain energy budget i.e., an RDE optimization. We considered energy by integrating power measurements from the system power supply unit. We present an RDE-optimized framework which allows for software-based real-time video compression, meeting the desired targets of electrical consumption, hence, controlling carbon emissions. The system can be made adaptive, dynamically tracking changes in image contents and in energy demands. We show results of energy-constrained compression wherein one can save as much as 31% of the power consumption with small impact on RD performance.