In this paper we present experimental results on electron beam pumping of MBE and MOVPE lasers with CdZnSe single quantum wells. Laser emission in the green and blue occurs under pulsed excitation, with threshold power densities typically less than 2 kW/cm2 at low temperatures. Threshold curves obtained at different electron beam energies show that there is an optimum electron beam energy for wells at a given depth below the surface. This suggests that it is possible to match the electron beam energy to a given structure. Results are broadly consistent with Monte Carlo calculations of the depth dependence of the energy deposition of the electron beam.