The 26Al–10Be burial dating method has been applied to a range of problems in geochronology. This technique allows us to determine the burial age of quartz-containing sediments, by measuring the concentration of cosmogenic 10Be and 26Al in the quartz. In its most basic form, the method assumes a simple history (single exposure episode followed by burial) for the quartz clasts. Balco and Rovey have recently developed an innovative isochron version of this method, which can take into account a more complicated exposure history for the quartz, and used it to date a series of glacial tills. There can be constraints on the slope and intercept of the isochron, depending on how we model the geology of the Balco–Rovey approach. We show how to take these constraints into account when fitting the slope and intercept; we apply a Bayesian approach, in which there is a straightforward way to implement constraints. We discuss the important issues that arise; a variety of choices must be made in choosing the prior, both in what geological insights to include and in how to include them. Copyright © 2011 John Wiley & Sons, Ltd.