It is well known that inference on the cointegrating relations in a vector autoregression (CVAR) is difficult in the presence of a near unit root. The test for a given cointegration vector can have rejection probabilities under the null, which vary from the nominal size to more than 90%. This paper formulates a CVAR model allowing for many near unit roots and analyses the asymptotic properties of the Gaussian maximum likelihood estimator. Then a critical value adjustment suggested by McCloskey for the test on the cointegrating relations is implemented, and it is found by simulation that it eliminates size distortions and has reasonable power for moderate values of the near unit root parameter. The findings are illustrated with an analysis of a number of different bivariate DGPs.