The emerging High Efficiency Video Coding (HEVC) standard is expected to require much more processing power than its predecessors due to the higher algorithmic complexity of new coding tools and associated data structures. This paper proposes a novel complexity control method for the near future HEVC encoders running on power-constrained devices. The proposed method is based on a decision algorithm that dynamically adjusts the depth of the Coding Units (CU) defined by quad-tree structures. New evidence about the relationship between CU depth and coding complexity is used to selectively constrain the CU depth in order to not exceed a predefined complexity target. The experimental results show that the encoder computational complexity can be downscaled by up to 60% at the cost of negligible loss of rate-distortion (RD) performance. The proposed method finds application in the near future multimedia portable devices using HEVC codecs.