A description is given of an advanced laboratory experiment in which the student is able to verify the Compton effect in detail. The experiment allows the student to examine the angular dependence of the energy of the Compton-scattered photon and of the Compton-scattered electron. The simultaneity of the two scattered “particles” is the key to the experimental observations. The results allow one to directly verify conservation of energy for single-photon scattering events. The agreement of experiment and theory then allow one to conclude that momentum is also conserved in these encounters.