States are developing new teacher evaluation systems that call for composite measures of teaching which combine information on student achievement growth with other metrics such as classroom observations and student surveys.  In this paper we discuss approaches to creating composite measures and focus on an approach that best predicts the underlying traits captured by the teacher metrics.  We discuss the difference of value weights, which are set by policymakers and define the criterion of interest, and empirical weights, which optimally weight the measures to produce the best prediction of the valued outcome.  Using new data from the Measures of Effective Teaching project, we empirically examine a number of composite specifications combining a variety of teacher measures including state test value added, supplemental low-stakes test value added, student perception surveys and multiple classroom observation protocols.  We discuss the implication of heterogenous and correlated measurement errors on the value of the empirical weights and the ability of the composite measure to distinguish top and bottom quartile teachers.