Evaluating the reliability of maturity level (ML) ratings is crucial for providing confidence in the results of software process assessments. This study investigates the dimensions underlying the maturity construct in the Capability Maturity Model (CMM) for Software (SW-CMM) and estimates the internal consistency of each dimension. The results suggest that SW-CMM maturity is a three-dimensional construct, with “Project Implementation” representing the ML 2 key process areas (KPAs), “Organization Implementation” representing the ML 3 KPAs, and “Quantitative Process Implementation” representing the KPAs at MLs 4 and 5. The internal consistency for each of the three dimensions as estimated by Cronbach’s alpha exceeds the recommended value of 0.9. Based on those results, this study builds and tests a theoretical model which posits that the achievement of lower ML KPAs sustains the implementation of higher ML KPAs. Results of path analysis using partial least squares (PLS) support the theoretical model and provide detailed understanding of the process improvement path. The analysis is based on 676 CMM-Based Appraisal for Internal Process Improvement (CBA IPI) assessments.