We propose a broadcast protocol that is based on a form of cooperative diversity called the Opportunistic Large Array (OLA). In the initial broadcast, an SNR ("transmission") threshold is used to define mutually exclusive sets of OLAs, such that the union of the sets includes all the nodes in the network. The broadcast protocol then basically alternates the transmitting set of nodes (or OLAs) during each broadcast cycle and is called Alternating OLA with Transmission Threshold (AOLA-T). Under A-OLA-T, broadcasting drains the energies of the nodes in the network efficiently and uniformly, extending the network life relative to broadcasts that use simple OLA or nonalternating OLAs with a transmission threshold. In this paper, we optimize the A-OLA-T protocol under the continuum assumption (very high node density).