Direct numerical simulations are used to study passive scalar transport and mixing in a round turbulent jet in a laminar crossflow. The velocity ratio of the jet to that of the crossflow is 5.7, the Schmidt number of the scalar is 1.49, and the jet-exit Reynolds number is 5000. The scalar field is used to compute entrainment of the crossflow fluid by the jet. It is shown that a bulk of this entrainment occurs on the downstream side of the jet. Also, the jet entrains a lot more than a simple jet even when the CVP is not yet formed and the jet has not yet bent into the crossflow. The reasons for a transverse jet's enhanced entrainment can be explained in terms of the pressure field around the jet. While the pressure gradient on the upstream side of the jet acts to bend it in the direction of the crossflow, the deformation of the jet's downstream side sets up a strong pressure gradient, that drives crossflow fluid toward the jet, resulting in increased entrainment.