Two algorithms to partition hole-free rectilinear polygons are developed. One has complexity ∼ O(kn) and the other O(n log k) where n is the number of vertices in the polygon and k is the smaller of the number of vertical and horizontal inversions of the polygon, k is a measure of the simplicity of a polygon. Since k is small for most practical polygons, our algorithms are fast in practice. Experimental results comparing our algorithms with that of Imai and Asano [1] are also presented.