  Aims: To incorporate background subtraction into the Bayesian Blocks
algorithm so that transient events can be timed accurately and precisely even
in the presence of a substantial, rapidly variable, background. Methods: We
developed several modifications to the algorithm and tested them on a simulated
XMM-Newton observation of a bursting and eclipsing object. Results: We found
that bursts can be found to good precision for almost all background
subtraction methods, but eclipse ingresses and egresses present problems for
most methods. We found one method that recovered these events with precision
comparable to the interval between individual photons, in which both source and
background region photons are combined into a single list and weighted
according to the exposure area. We have also found that adjusting the Bayesian
Blocks change points nearer to blocks with higher count rate removes a
systematic bias towards blocks of low count rate.
