The case of a strong contestant who has no direct way to demonstrate i
ts strength and may have to send a costly signal to prove it appears f
requently in the signalling literature. We examine what occurs in sign
alling models with two or more contestants. The receiver of the signal
may serve as a credible coordinator who punishes the senders for not
collaborating with each other, the result being a separating equilibri
um in which the signal sent by the strong contestants, though costly,
is also quite rewarding: it increases their payoff level over and abov
e the level attained when their strength is common knowledge.