We introduce a new problem of broadcast source coding with a discrimination requirement - there is an eavesdropping user from whom we wish to withhold the true message in an entropic sense. Binning can achieve the Slepian-Wolf rate, but at the cost of full information leakage to the eavesdropper. Our main result is a lower bound that implies that any entropically efficient broadcast scheme must be "like binning" in that it also must leak significant information to eavesdroppers.