Binarization of document images is one of the most relevant pre-processing operations, leading to a significant decrease of the amount of information used during their further analysis. Since many document images, particularly historical, may be degraded over time, the application of some simple global thresholding methods usually lead to highly unsatisfactory results. A similar situation may occur for unevenly illuminated images, limiting the visibility of various shapes, representing not only the alphanumerical characters. A typical solution of this problem is the application of some adaptive thresholding methods, as well as more sophisticated solutions, proposed recently e.g. during Document Image Binarization Competitions (DIBCO) or TQ-DIB 2019 competition. Nevertheless, due to their relatively high computational demands, there is still a need of some faster methods, leading to high binarization accuracy for challenging benchmark datasets, such as DIBCO or Nabuco. Hence, the adaptation and optimization of the parameters of the fast thresholding method utilizing background estimation, proposed originally for the OCR purposes and verified for unevenly illuminated printed documents, is presented in this paper. The proposed solution has been optimized and verified using the state-of-the-art datasets containing 166 degraded document images together with their ground-truth binary equivalents, leading to better results, also in comparison to much slower adaptive thresholding methods. The performance of all methods used in comparisons has been determined using commonly accepted metrics, such as F-Measure, Accuracy, Distance Reciprocal Distortion (DRD) or Misclassification Penalty Metric (MPM), and relative execution time, calculated for all used image datasets.