In this paper we present a computationally efficient algorithm for reducing the blocky and Gibbs oscillation artifacts commonly present in JPEG compressed images. The algorithm alpha-blends a smoothed version of the image with the original image; however, the blending is controlled by a limit factor that considers the amount of compression present and any local edge information derived from the application of a Prewitt filter. In addition, the actual value of the blending coefficient (α) is derived from the local Mean Structural Similarity Index Measure (MSSIM) which is also adjusted by a factor that also considers the amount of compression present. We also present our results as well as the results for a variety of other papers whose authors used other post compression, filtering methods.