Summary: A transmission control strategy is described for slotted-ALOHA-type broadcast channels with ternary feedback. At each time slot, each station estimates the probability that n stations are ready to transmit a packet for each \(n\), using Bayes' rule and the observed history of collisions, successful transmissions, and holes (empty slots). A station transmits a packet in a probabilistic manner based on these estimates. This strategy is called Bayesian broadcast. An elegant and very practical strategy -- pseudo-Bayesian broadcast -- is then derived by approximating the probability estimates with a Poisson distribution with mean \(\nu\) and further simplifying. Each station keeps a copy of \(\nu\), transmits a packet with probability \(1/\nu\), and then updates \(\nu\) in two steps: For collisions, increment \(\nu\) by \((e-2)^{-1}=1.39221\ldots\). For successes and holes, decrement \(\nu\) by 1. Set \(\nu\) to \(\max(\nu + \hat{\lambda}, 1)\), where \(\hat{\lambda}\) is an estimate of the arrival rate \(\lambda\) of new packets into the system. Simulation results are presented showing that pseudo-Bayesian broadcast performs well in practice, and methods that can be used to prove that certain versions of pseudo-Bayesian broadcast are stable for \(\lambda < e^{-1}\) are discussed.