The fluctuations in the network bandwidth during video streaming are currently addressed through HTTP adaptive streaming [2]. However, it currently lacks the necessary awareness to alter the video content based on its decoding-complexity to reduce the energy demand on the end user's device. (The term decoding-complexity in this manuscript refers to the number of CPU instructions consumed by the processor to decode an encoded bit stream.) This will become more pronounced with time, especially due to the complexity of modern standards such as High Efficiency Video Coding (HEVC) and the upcoming Versatile Video Coding (VVC), and the increasing demand for high definition (HD) content on hand-held devices [3; 4]. As a solution, simultaneous control of both bit rate and decoding-complexity of an encoded video sequence could potentially address both these constraints. For instance, such an algorithm could generate bit streams with arbitrary bit rates and decoding-complexity levels that could be used with HTTP adaptive streaming where the requested bit stream segments are adapted based on both network bandwidth and the device's remaining energy constraints. Yet, thus far, this has not been considered in the literature. Broadly, the state-of-the-art attempts to reduce decoding-complexity include efficient decoder implementations [5; 6; 7; 8], dynamic alterations to the decoding process [9], dynamic voltage and frequency scaling (DVFS) methods [10; 11; 12; 13], content adaptation based on scalable coding architectures [14; 15; 16], and media transcoding [17] approaches. Out of these, the latter two are encoder-side operations, and operate together with HTTP adaptive streaming solutions such as MPEG-DASH [2; 18] to fetch videos of different decoding-complexities based on a device's remaining energy level. However, existing content adaptation algorithms simply manipulate the bit rate, quantization parameter (QP), spatial resolution, etc., in an attempt to reduce the decoding-complexity and the device's energy consumption [19; 20; 21; 22; 23], which eventually results in poor visual quality and minimal decoding-complexity reductions. In contrast to these approaches, the authors' previous work in [24] proposes a decoding-complexity-rate-distortion model within the encoder to determine the coding modes that minimize the joint rate, decoding-complexity, and distortion cost for a given QP. However, the deficiencies of the basic concept in [24] could be traced back to the lack of simultaneous allocation and control of the bit rate and the decoding-complexity levels (e.g., being able achieve multiple arbitrary decoding-complexities at the same bit rate) for rate and decoding-complexity-controlled video coding--an aspect that is also overlooked in the literature and that is developed in this work [3]. In this context, this paper proposes a novel joint coding tree unit (CTU)-level decoding-complexity and rate-controlled encoding algorithm for HEVC. This includes, (i) a decoding-complexity-rate-distortion model along with a mode selection cost function that incorporate both bit rate and decoding-complexity as constraints. Furthermore, a (ii) mean square error (MSE)-based algorithm that utilizes the proposed decoding-complexity-rate-distortion model is proposed to allocate bits and decoding-complexity levels across frames and CTUs. Finally, (iii) a content-adaptive, CTU-level, decoding-complexity-controlled video coding algorithm that derives the appropriate coding parameters and trade-offs for bit rate and decoding-complexity, is proposed to meet the constraints imposed on the bit rate and decoding-complexity with minimal distortion. The remainder of the paper is organized as follows. An overview of state-of-the-art is presented in Section 2, followed up by a detailed description of the decoding-complexity, rate, and distortion model in Section 3. Section 4 describes the proposed joint decoding-complexity and rate control algorithm.