The increased complexity of performance-sensitive soft- ware systems leads to increased use of automated adapta- tion policies in lieu of manual performance tuning. Com- position of adaptive components into larger adaptive sys- tems, however, presents challenges that arise from potential incompatibilities among the respective adaptation policies. Consequently, unstable or poorly-tuned feedback loops may result that cause performance deterioration. This paper (i) presents a mechanism, called adaptation graph analy- sis, for identifying potential incompatibilities between com- posed adaptation policies and (ii) illustrates a general de- sign methodology for co-adaptation that resolves such in- compatibilities. Our results are demonstrated by a case study on energy minimization in multi-tier Web server farms subject to soft real-time constraints. Two independently effi- cient energy saving policies (an On/Off policy that switches machines off when not needed and a dynamic voltage scal- ing policy) are shown to conflict leading to increased en- ergy consumption when combined. Our adaptation graph analysis predicts the problem, and our co-adaptation design methodology finds a solution that improves performance. Experimental results from a 17-server farm running the in- dustry standard TPC-W e-commerce benchmark show that co-adaptation renders a cut-down in energy consumption by more than 50%, when workload is not high, while main- taining latency within acceptable bounds. The paper serves as a proof of concept of the proposed conflict-identification and resolution methodology and an invitation to further in- vestigate a science for composing adaptive systems.