Software development organizations that rely on Capability Maturity Model Integration (CMMI) to assess and improve their processes have realized that agile approaches can provide improvements as well. CMMI and agile methods can work well together and exploit synergies that have the potential to improve dramatically business performance. The major question is: How to realize the integration of these two seemingly different approaches? In an earlier work, we have conducted a field study within six companies. These companies worked with agile methods for years and the Egyptian Software Engineering Competence Center (SECC), which is the regional CMMI appraisal center, assessed them. This study was mainly conducted to enhance the empirical understanding in this research field. Additionally, it showed that companies usually don't use agile in a good way that helps in covering the CMMI specific practices. In this paper, we present a new approach for mapping between CMMI and Scrum method. This mapping has been analyzed, enhanced, and then applied to the same companies. Putting in considerations that other previous efforts have worked in the same context but for an older version of CMMI, our research is using the latest CMMI version, which is 1.3. The research shows that our mapping approach has resulted in 37% satisfaction and achieved 17% partial satisfaction for CMMI specific practices. This resembles 19.4% enhancement in the satisfaction, and 6.2% improvement in the partial satisfaction against the previous related research effort that was already not targeting the latest CMMI version.