Direct numerical simulation is used to study the effect of entrainment near the inflow nozzle on spatially evolving round jets. Inflow entrainment is obtained by providing a buffer region upstream of the inflow nozzle. Simulations are performed at Reynolds numbers of 300 (laminar) and 2400 (turbulent), respectively. Simulations without the inflow buffer are contrasted to those with the buffer region. The potential core is seen to close earlier in th presence of inflow entrainment. As a result, near-field turbulent intensities and pressure fluctuations on the jet centerline are noticeably affected. It is suggested that inflow entrainment results in an effective co-flow, whose effect on the volumetric flow rate near the inflow nozzle is appreciable for both laminar and turbulent jets. When plotted in similarity variables, the far-field solutions with and without inflow entrainment agree well with each other, and experiment. The results suggest the importance of allowing for inflow entrainment in simulations of turbulent jets, particularly for studies where near-field behavior is important.