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CMMI® has proven benefits in software process improvement. Typically, organisations that achieve a CMMI level rating improve their performance. However, CMMI implementation is not trivial, in particular for high maturity levels, and not all organisations achieve the expected results. Certain CMMI implementation problems may remain undetected by SCAMPISM since only a sample of the organisation is analysed during the appraisal and assessing the quality of implementation of some practices may be difficult. In this paper we present the case of three CMMI level 5 organisations. From the lessons learnt and based on an extensive bibliographic research, we identify a set of problems and difficulties that organisations willing to implement CMMI should be aware of and provide a set of recommendations to help avoid them. As future research we will develop a framework to help to evaluate the quality of implementation of CMMI practices.