This paper considers alternative methods of testing cointegration in fractionally integrated processes, using the bootstrap. The investigation focuses on the issues of (a) choice of statistic, (b) bias correction techniques, and also (c) designing the simulation of the null hypothesis. The latter consideration is crucial for ensuring tests are both correctly sized and powerful. Three tests are considered, one for null of cointegration, all based on residuals from a putative cointegrating regression. The tests are compared in Monte Carlo experiments whose main object is to throw light on the relative roles of issues (a), (b) and (c) in test performance.