The paper investigates the predictive performance of different explicit Reynolds-stress closure models when applied to the simulation of 3D wall jets. The flow is of particular interest for its remarkably large ratio of lateral to normal spreading. Experiments report that the lateral rate of spread exceeds the wall-normal rate of spread between five and nine times. This phenomenon is often vigorously misrepresented by RANS simulations. There exists some body of evidence suggesting that the large lateral spreading is due to significant amounts of turbulence-driven axial vorticity (J. Fluid Mech. 435 (2001) 305). The origin of the axial vorticity can be traced back to the anisotropy of turbulent normal stresses perpendicular to the jet axis. The present paper assess the ability of explicit stress-strain relationships to mimic the normal-stress anisotropy in 3D wall jets. It is shown that linear Boussinesqviscosity models inevitably fail to render the spreading mechanism. Moreover, the paper argues that a physically sound modelling of 3D wall jets requires an explicit closure to include at least one quartic term.