This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004). The class of tests covered by this admissibility result contains the Anderson and Rubin (1949) test. Thus, there is no conventional statistical sense in which the Anderson and Rubin (1949) test "wastes degrees of freedom". In addition, it is shown that the test proposed by Moreira (2003) belongs to the closure of (i.e., can be interpreted as a limiting case of) the class of tests covered by our admissibility result. Keywords: Instrumental Variables, Regression, Inference. JEL Classifications: C13, C14, C30, C51, D4, J24, J31.