The increasing processing speed of computers has made software-based video coding possible. Several reports have been published on increasing the processing speed of such video coding through improved software development techniques, and on increasing video coding speed by efficiently omitting the video coding process itself. However, the actual speed of software-based video coding depends on the implementation environments. Accordingly, under some environments of lower processing speed, the processor can not encode video data in real time, even if real-time coding is necessary. This has created a need to control a video coding process with depending on the processing speed. To address this need, we propose a new scheme for controlling motion estimation. This scheme, which we call "time adaptive motion estimation" (TAME), is based on the Successive Elimination Algorithm (SEA) method. It enables motion estimation to be completed within a pre-determined target time. Computer simulation results demonstrate that the proposed method achieves nearly the same quality as in the case where coding time is unlimited.