From the literature, it is demonstrated that performing text-line segmentation directly in the run-length compressed handwritten document images significantly reduces the computational time and memory space. In this paper, we investigate the issues of word and character segmentation directly on the run-length compressed document images. Primarily, the spreads of the characters are intelligently extracted from the foreground runs of the compressed data and subsequently connected components are established. The spacing between the connected components would be larger between the adjacent words when compared to that of intra-words. With this knowledge, a threshold is empirically chosen for inter-word separation. Every connected component within a word is further analysed for character segmentation. Here, min-cut graph concept is used for separating the touching characters. Over-segmentation and under-segmentation issues are addressed by insertion and deletion operations respectively. The approach has been developed particularly for compressed handwritten English document images. However, the model has been tested on non-English document images.