Retinex theory was among the first to introduce a model for simultaneous brightness adjustment and removal of illumination influence on image colors by supposedly emulating some aspects of the human visual system's behaviour. The main idea of most Retinex methods is to readjust color channel values of individual pixels with respect to their local white references. Recently the Smart Light Random Memory Sprays Retinex (SLRMSR) method with a O(1) per-pixel complexity was proposed. Although theoretically fast, like with many other Retinex methods, the problem is that its local pixel sampling scheme and some of its local maximum calculation structures common to other Retinex methods as well are not particularly hardware-friendly. In this paper a reduced sampling scheme and an approximated local maxima calculation are proposed and included into a modified SLRMSR. While the resulting images are visually very similar to the ones obtained by the original SLRMSR, the modified SLRMSR is structurally simpler and more hardware friendly. The results are presented and discussed.