After graduating in 1995, Dexter's early successes were on stage, in particular with two high-profile productions of Tennessee Williams plays, beginning with Sam Mendes' 1995 Olivier Award-winning production of The Glass Menagerie at the Donmar Warehouse, in which he played Jim O'Connor. This was soon followed by Trevor Nunn's Tony Award-winning production of Williams' never-before-seen Not About Nightingales, which transferred from London's National Theatre to the Circle in the Square Theatre on Broadway in 1999.