Managing a patient with comorbid diseases according to multiple clinical practice guidelines (CPGs) may result in adverse interactions that need to be mitigated (identified and addressed) so a safe therapy can be devised. However, mitigation poses both clinical and methodological challenges. It requires extensive domain knowledge and calls for advanced CPG models and efficient algorithms to process them. We respond to the above challenges by describing our algorithm that mitigates interactions between pairs of CPGs. The algorithm creates logical models of analyzed CPGs and uses constraint logic programming (CLP) together with domain knowledge, codified as interaction and revision operators, to process them. Logical CPG models are transformed into CLP-CPG models that are solved to find a safe therapy. We represent these CLP-CPG models using MiniZinc, a standard language for CLP models. As motivation and illustration of our mitigation algorithm we use a clinical case study describing a patient managed for hypertension and deep vein thrombosis according to two individual CPGs. We apply the algorithm to this scenario and present MiniZinc representations of the constructed CLP-CPG models.