The stability limits of a turbulent flame in a practical combustor are important characteristics that influence its performance. The mechanisms controlling the stability limits of turbulent non-premixed flames are examined here in the canonical configuration of a fuel jet in co-flow air. This study focuses on the conditions leading to the detachment of flames from the injector nozzle by means of an experimental parametric study in which pressure (1 <= P <= 10 bar), fuel (methane and ethane), nozzle wall thickness (t = 0.20 mm, 0.58 mm, and 0.89 mm), jet velocity (0.5 <= U-j <= 16.5 m s(-1)), and co-flow velocity (U-c = 0.3 m s(-1), 0.6 m s(-1), and 0.9 m s(-1)) are varied. It is shown that the mechanism leading to detachment depends on the ratio of the nozzle wall thickness to the laminar flame thickness. If this ratio is smaller than 3, the nozzle is thin and type I detachment occurs (flame base stability lifting). In this case, the detachment velocity decreases with pressure and is proportional to the laminar burning velocity. If the ratio is larger than 3, the nozzle is "thick" and type II detachment occurs (local flame extinction lifting). Then, the detachment velocity is controlled by the extinction strain rate. Experiments also show that the Kolmogorov scale of turbulence regulates local flame extinction and type II detachment and a model is proposed to predict detachment for any fuel, pressure, and nozzle wall thickness using the computed extinction strain rate and the Kolmogorov time scale. Finally, the data show that elevating pressure allows stabilizing attached non-premixed jet flames with high Reynolds numbers without the need for complex stabilization strategies such as pilot flames, swirl, or oxygen/hydrogen enrichment. Pressure allows studying flame/turbulence interactions at Reynolds numbers relevant to practical applications while conserving simple configurations amenable to diagnostics and modeling. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.