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Geocasting is a variation of traditional multicasting in which the goal is to deliver a packet to all nodes within a geographical area often referred to as a geocast region. Several protocols have been designed for geocasting in mobile ad hoc networks (MANETs) which focus on how to route packets to the geocast region efficiently, while packet delivery within the geocast region is usually achieved by flooding. Given the known limitations of simple flooding on a network, it is beneficial to look for solutions that improve the packet delivery mechanism within a geocast region. In this paper, a protocol is proposed that extends existing geocast protocols by supporting a novel packet delivery mechanism through the use of efficient flooding. The solution employs coverage information and partitioning the geocast region into grids. Using coverage information, only nodes that can reach the new portion of the region, which has not been covered by a transmission, will rebroadcast the packet. The paper shows that this solution is superior to simple flooding since it reduces the number of redundant retransmissions within the geocast region considerably.