Non-Gaussian noise transients in interferometric gravitational-wave detectors increase the background in searches for short-duration and un-modelled signals. We describe a method for vetoing noise transients by ranking the statistical relationship between triggers in auxiliary channels that have negligible sensitivity to gravitational waves and putative gravitational-wave triggers in the detector output. The novelty of the algorithm lies in its hierarchical approach, which leads to a minimal set of veto conditions with high performance and low deadtime. After a given channel has been selected it is used to veto triggers from the detector output, then the algorithm selects a new channel that performs well on the remaining triggers and the process is repeated. This method has been demonstrated to reduce the background in searches for transient gravitational waves by the LIGO and Virgo collaborations.