High-redshift quasars (HZQs) with redshifts of z ≳ 6 are so rare that any photometrically selected sample of sources with HZQ-like colours is likely to be dominated by Galactic stars and brown dwarfs scattered from the stellar locus. It is impractical to re-observe all such candidates, so an alternative approach was developed in which Bayesian model comparison techniques are used to calculate the probability that a candidate is a HZQ, Pq, by combining models of the quasar and star populations with the photometric measurements of the object. This method was motivated specifically by the large number of HZQ candidates identified by cross-matching the UKIRT (United Kingdom Infrared Telescope) Infrared Deep Sky Survey (UKIDSS) Large Area Survey (LAS) to the Sloan Digital Sky Survey (SDSS): in the covered by the LAS in the UKIDSS Eighth Data Release (DR8) there are ∼9 × 103 real astronomical point sources with the measured colours of the target quasars, of which only ∼10 are expected to be HZQs. Applying Bayesian model comparison to the sample reveals that most sources with HZQ-like colours have Pq≲ 0.1 and can be confidently rejected without the need for any further observations. In the case of the UKIDSS DR8 LAS, there were just 107 candidates with Pq≥ 0.1; these objects were prioritized for re-observation by ranking according to Pq (and their likely redshift, which was also inferred from the photometric data). Most candidates were rejected after one or two (moderate-depth) photometric measurements by recalculating Pq using the new data. That left 12 confirmed HZQs, six of which were previously identified in the SDSS and six of which were new UKIDSS discoveries. The high efficiency of this Bayesian selection method suggests that it could usefully be extended to other HZQ surveys (e.g. searches by the Panoramic Survey Telescope And Rapid Response System, Pan-STARRS, or the Visible and Infrared Survey Telescope for Astronomy, VISTA) as well as to other searches for rare objects.