—High Efficiency Video Coding (HEVC) is one of the latest released video standards and offers up to 40% bitrate savings when compared to the widespread H.264/AVC standard, at the cost of a substantial complexity growth. Constraining the complexity of HEVC encoding is a challenging task for embedded applications based on a software encoder. The most frequent approach to solve this problem is to optimise the coding tree structure to balance compression efficiency and computational complexity. In this context, we propose and assess a method to adequately allocate the computational complexity among coding units in a frame encoded in Intra mode. By studying an open-source real-time HEVC encoder, correlations are observed between Rate-Distortion (RD)-cost and encoding complexity that motivate a new complexity allocation technique. This technique, called " Constrain the Docile CTUs " (CDC), consists of allocating less computational complexity to units with low RD-costs and using RD-costs from preceding images as predictors for the current RD-costs. Experimental results demonstrate substantial gains, up to 36% of Bjøntegaard Delta Bit Rate (BD-BR), when using CDC method instead of other allocation methods.