The near-field behavior of coaxial jets is studied through direct numerical simulation (DNS) with a particular focus on the influence of the inner shear layer steepness characterized by its momentum thickness θ01 thus mimicking the variation in the lip thickness of a real jet nozzle. We investigate the two distinct jet regimes ru>ruc for which a recirculation bubble is present near the jet inlet and ruruc case, variations of θ01 strongly affect the shape and the downstream extent of the recirculation bubble. The DNS allow to show the strong dependency of the inner and outer potential core lengths and of the critical value ruc on the jet inlet velocity profile. We finally revisit the theoretical model originally proposed by Rehab, Villermaux, and Hopfinger [“Flow regimes of large-velocity-ratio coaxial jets,” J. Fluid Mech. 345, 357 (1997)] first aimed at the prediction of the variations of various jet characteristics as a function of ru. The model is extended to determine the dependency of the jet characteristics with θ01. A very good correspondence between the theoretical predictions and the numerical results is obtained.