Recirculating hot combustion products play an essential role in the stabilization of diffusion flames in a combustor. An idealized one-dimensional configuration is utilized to elucidate this process. It consists of three parallel streams: to the left, a layer of fuel at subignition temperature; an intermediate finite thickness layer of oxidizer at the same low temperature; and to the right, a layer of hot combustion products. Using numerical simulations, three distinct ignition regimes are identified as the thickness of the intermediate layer is decreased, with corresponding ignition time variations spanning several orders of magnitude. The main speed-up mechanism is attributed to the abrupt transition from ignition via a classical triple flame at the fuel-oxidizer boundary, to ignition at a competing site located at the boundary between the cold oxidizer and the hot products. High activation energy asymptotics leads to a practical procedure to relate the intermediate layer thickness and the ignition time.