Small deviations from exact u nit roots can product large coverage rate distortions for conventional confidence sets for cointegrating coefficients (Elliott ). We therefore propose new methods for constructing confidence sets for long-run coefficients with highly serially correlated regressors which do not necesarilly have a unit root. Although the standard boostrap is shown to be asytmptotically invalid, a modified, valid boostrap is developed. invariant confidence sets that are option (highest average accuracy) are obtained but are difficult to implement in practice. An approximately optimal invariant method is proposed; this works almost as well as the optimal method, at least for a single persistent regressor.