Instrumental variables estimation is classically employed to avoid simultaneous equations bias in a stable environment. Here we use it to improve upon ordinary least squares estimation of cointegrating regressions between nonstationary and/or long memory stationary variables where the integration orders of regressor and disturbance sum to less than 1, as happens always for stationary regressors, and sometimes for mean-reverting nonstationary ones. Unlike in the classical situation, instruments can be correlated with disturbances and/or uncorrelated with regressors. The approach can also be used in traditional non-fractional cointegrating relations. Various choices of instrument are proposed. Finite sample performance is examined.