This paper provides a new approach to testing cointegration parameters in a single-equation cointegration environment. The novelty is in improving over the well-known heteroscedasticity and autocorrelation consistent (HAC) robust standard errors using fixed bandwidth (fixed-b) asymptotic theory and adapting it to the cointegration environment. It is shown that the standard tests still have asymptotic distributions free of serial correlation nuisance parameters regardless of the bandwidth or kernel used, even if the regressors in the cointegration relationship are endogenous. Using asymptotic power and finite sample size simulation experiments, a specific kernel and bandwidth choice is recommended. Finite sample simulations comparing the size and power of the test using the fixed-b asymptotics to some of the currently popular tests are performed. These simulations confirm that the well-known size distortion of the standard tests can be greatly reduced. Finally, the newly developed test is employed to investigate the standard money-demand relationship for US data.