The increased complexity of performance-sensitive software systems leads to increased use of automated adaptation policies in lieu of manual performance tuning. Composition of adaptive components into larger adaptive systems, 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 analysis, for identifying potential incompatibilities between composed adaptation policies and (ii) illustrates a general design methodology for co-adaptation that resolves such incompatibilities. 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 efficient energy saving policies (an On/Off policy that switches machines off when not needed and a dynamic voltage scaling policy) are shown to conflict leading to increased energy 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 industry 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 maintaining 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 investigate a science for composing adaptive systems.