It is well known that the performance of context-based image processing systems can be improved by allowing the processor (e.g., an encoder or a denoiser) a delay of several samples before making a processing decision. Often, however, for such systems, traditional delayed-decision algorithms can become computationally prohibitive due to the growth in the size of the space of possible solutions. In this paper, we propose a reduced-complexity, one-pass, delayed-decision algorithm that systematically reduces the size of the search space, while also preserving its structure. In particular, we apply the proposed algorithm to two examples of adaptive context-based image processing systems, an image coding system that employs a context-based entropy coder, and a spatially adaptive image-denoising system. For these two types of widely used systems, we show that the proposed delayed-decision search algorithm outperforms instantaneous-decision algorithms with only a small increase in complexity. We also show that the performance of the proposed algorithm is better than that of other, higher complexity, delayed-decision algorithms.