The reasons that drive construction companies to innovate, as well as the processes they use, have not yet been fully explored in the construction management literature. This paper describes the “hows” and “whys” behind the push for innovation in a construction company. The research method is founded on the validation of a model developed by a case study; this is focused on a medium-sized construction company which implemented and certified an innovation management system, as established by a Spanish standard. The studies conducted by the authors over a five-year period generated a set of 18 propositions reflecting an explanatory model of innovation management. This paper reports on the external validation of this model by means of a set of interviews; the results fully corroborate 15 of these propositions. The strongest drivers of innovation in construction companies are technical problems in construction projects, client requirements, and upper management. Innovation opportunities are identified as a result of examination of the internal processes of the company, the construction projects, and the environment. Identifying, developing, and transferring an innovative solution require the implementation of technological watch and knowledge management in the organization. Finally, the research concludes that the main benefit of innovation management is an increase in the company’s technical capability, whereas the two main barriers to innovation are the prioritization of production processes and the lack of support from the leaders of the company.