We present the identifications of two z ~ 3·8 quasars from a deep UBI imaging survey with the Palomar 5·1 m Telescope. The survey covers an area of 0·25 degree2 around a sample of ten z =0·2–0·3 luminous X-ray clusters. The QSOs were identified on the basis of their stellar morphologies, relatively blue optical and very red UV–optical colours. The two objects are Q 1322+5034, with total magnitudes of B =20·8, I =18·3 and (U–B) > 4·7, and Q 1722+3211, which has total magnitudes of B =21·8, I =19·7 and (U–B) > 3·2. Subsequent spectroscopic observations with the 4·2 m William Herschel Telescope have confirmed the identity of these two sources as QSOs at z =3·82 and z =3·73 respectively. Our spectroscopic observations identify a damped Lyman-α absorber in the spectrum of Q 1322+5034 at z =3·439, as well as a second absorption system at z =2·700, which may be either a single very high column density, damped Lyman-α system, or more likely a blend of a number of high column-density absorbers spread over a distance of ~10 Mpc.