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This paper presents a computationally-scalable motion estimation (ME) algorithm in which it can dynamically control the number of operations spent on ME while the compressed video quality, in terms of PSNR and bit rate, will be scaled up or down smoothly. Unlike fast search algorithms, our proposed algorithm employs a closed-loop control to adaptively adjust the search strategy so that the actual ME computational complexity can be kept close to the allocated budget as much as possible. Experimental results show that when the ME computational budget falls to half of the average number of operations required by the fast full search (for the best quality), on average, the PSNR is reduced by 0.046dB and the bit rate is increased by 2.34% as compared to that of full search for 1920x1080 video sequences and this computationally-scalable ME algorithm is particularly suitable for consumer devices to realize real-time computational budget control for video compression.