Removing the influence of illumination on image colors and adjusting the brightness across the scene are important image enhancement problems. This is achieved by applying adequate color constancy and brightness adjustment methods. One of the earliest models to deal with both of these problems was the Retinex theory. Some of the Retinex implementations tend to give high-quality results by performing local operations, but they are computationally relatively slow. One of the recent Retinex implementations is light random sprays Retinex (LRSR). In this paper, a new method is proposed for brightness adjustment and color correction that overcomes the main disadvantages of LRSR. There are three main contributions of this paper. First, a concept of memory sprays is proposed to reduce the number of LRSR's per-pixel operations to a constant regardless of the parameter values, thereby enabling a fast Retinex-based local image enhancement. Second, an effective remapping of image intensities is proposed that results in significantly higher quality. Third, the problem of LRSR's halo effect is significantly reduced by using an alternative illumination processing method. The proposed method enables a fast Retinex-based image enhancement by processing Retinex paths in a constant number of steps regardless of the path size. Due to the halo effect removal and remapping of the resulting intensities, the method outperforms many of the well-known image enhancement methods in terms of resulting image quality. The results are presented and discussed. It is shown that the proposed method outperforms most of the tested methods in terms of image brightness adjustment, color correction, and computational speed.