This work examines the problem of providing reliable broadcast delivery of messages with minimal communication overhead in wireless networks. We consider two types of communication for broadcasting: one-to-all (the classical form of broadcasting where each node forwards the message to all its neighbours with one transmission) and one-to-one (each transmission forwards the message to only one neighbour at a time). We propose to reduce the communication overhead involved in both these forms of broadcasting by applying the concept of internal nodes. We simulate and analyze the performance of a family of three algorithms we propose for the one-to-all model using internal nodes. Neighbour elimination is used to reduce redundant rebroadcasts, and reliability is almost guaranteed with the introduction of RANA (Retransmission after negative acknowledgement). For the one-to-one model, in addition to applying the internal nodes concept, three additional algorithms P-broadcast, IP-broadcast and PI-broadcast are proposed based on the concept of planar subgraphs such as RNG (relative neighbourhood graphs). We compare the relative performance of these proposed approaches against those presented in literature. (Abstract shortened by UMI.)