Likelihood ratio (LR) tests for the cointegrating rank of a vector autoregressive (VAR) process have been developed under different assumptions regarding deterministic terms. For instance, nonzero mean terms and linear trends have been accounted for in some of the tests. In this paper we provide a general framework for deriving the local power properties of these tests. Thereby it is possible to assess the virtue of utilizing varying amounts of prior information by making assumptions regarding the deterministic terms. One interesting result from this analysis is that if no assumptions regarding the specic form of the mean term are made while a linear trend is excluded then a test is available which has the same local power as an LR test derived under a zero mean assumption.