We evaluate by Monte Carlo simulation the empirical sizes of Johansen's likelihood ratio tests for the number of cointegrating vectors using his tabulated asymptotic critical values. The powers of these tests and of the Dickey-Fuller and cointegrating regression Durbin-Watson tests for cointegration are compared in an experimental design where more than one cointegrating vector is possible, and where there is a possible mismatch between the variables used in the construction of the tests and the variables entering the true cointegrating vector(s). This analysis allows for potential overspecification or underspecification of the variables included in a cointegration analysis.