We consider in this paper a variation of Csiszár and Körner's model of broadcast channels with confidential messages. The transmitter sends both a confidential message and a non-confidential message (herein termed as public message) to receiver 1. While receiver 2 should be kept ignorant from the confidential message, we do not impose the requirement that the public message needs to be perfectly recovered by receiver 2. This more liberal treatment of the non-confidential message is perhaps a more reasonable model than Csiszár and Körner's model where the non-confidential message is required to be decoded by both receivers. Measuring ignorance by equivocation rate Re, a single-letter characterization is given of the achievable triples (R1, Re, Rp) where R1 and Rp are respectively the confidential and public message rates.