Batch effects are a persistent and pervasive form of measurement noise which undermine the scientific utility of high-throughput genomic datasets. At their most benign, they reduce the power of statistical tests resulting in actual effects going unidentified. At their worst, they constitute confounds and render datasets useless. Attempting to remove batch effects will result in some of the biologically meaningful component of the measurement (i.e. signal) being lost. We present and benchmark a novel technique, called Harman. Harman maximises the removal of batch noise with the constraint that the risk of also losing biologically meaningful component of the measurement is kept to a fraction which is set by the user.