Establishing a research strategy that is suitable for undertaking research on software engineering is vital if we are to guarantee that research products are developed and validated following a systematic and coherent method. We took this into account as we carried out the COMPETISOFT research project, which investigated software process improvement (SPI) in the context of Latin American small companies. That experience has enabled us to develop a research strategy based on the integrated use of action research and case study methods. This paper introduces the proposed research strategy and provides extensive discussion of its application for: (1) developing the Methodological framework of COMPETISOFT for SPI, (2) putting this framework into practice in eight small software companies, and (3) refine the Methodological framework due to the practice feedback. The use of this research strategy allowed us to observe that it was suitable for developing, refining, improving, applying, and validating COMPETISOFT's Methodology framework. Furthermore, having seen it applied, we believe that this strategy offers a successful integration of action research and case study, which can be useful for conducting research in other software engineering areas which address needs of small software companies.