transmitting conflicts in a peer to peer simple network

I have a 3 node P2P setup with 2 nodes transmitting and one node on an ATmega 32 receiving the data. The transmitters are completely asynchronous and could transmit while the other transmitter is also transmitting.
What happens in that situation? The packets are small, in the order of 16 bytes at 19200 baud. From reading the datasheet it seems as though the 2nd transmitter should simply wait until the ether clears and then transmit, but periodically I do miss a transmission. For any one transmitter there is at least a 5 second delay before the next packet is ready to transmit, so there is not a heavy load on the system.
Any thoughts would be greatly appreciated. Targeting an article in Nuts and Volts for this project.