Vehicle safety communication applications require safety messages to be received by all the targeted vehicles within their lifetime. We propose a piggybacked cooperative repetition approach for reliably broadcasting safety messages in VANETs. Repetitions by neighbors that receive the original transmission can effectively cover the areas that are missed in the original transmissions. Moreover, the repetitions are piggybacked by the newly generated messages so that no extra messages are injected into the network. Our experiments show a significant performance improvement, achieving over 90% reception rate of safety messages at distances up to 200 meters to the sender.