The concept of cis-regulatory modules located in gene promoters represents today’s vision of the organization of gene transcriptional regulation. Such modules are a combination of two or more single, short DNA motifs. The bioinformatic identification of such modules belongs to so-called NP-hard problems with extreme computational complexity, and therefore, simplifications, assumptions, and heuristics are usually deployed to tackle the problem. In practice, this requires, first, many parameters to be set before the search, and second, it leads to the identification of locally optimal results. Here, a novel method is presented, aimed at identifying the cis-regulatory elements in gene promoters based on an exhaustive search of all the feasible modules’ configurations. All required parameters are automatically estimated using positive and negative datasets. To be computationally efficient, the search is accelerated using a multidimensional hash function, allowing the search to complete in a few hours on a regular laptop (for example, a CPU Intel i7, 3.2 GH, 32 Gb RAM). Tests on an established benchmark and real data show better performance of BestCRM compared to the available methods according to several metrics like specificity, sensitivity, AUC, etc. A great practical advantage of the method is its minimum number of input parameters—apart from positive and negative promoters, only a desired level of module presence in promoters is required.