Many prey species use colourful 'aposematic' signalling to advertise the fact that they are toxic. Some recent studies have shown that the brightness of aposematic displays correlates positively with the strength of toxicity, suggesting that aposematic displays are a form of handicap signal, the conspicuousness of which reliably indicates the level of toxicity. The theoretical consensus in the literature is, however, at odds with this finding. It is commonly assumed that the most toxic prey should have less bright advertisements because they have better chances of surviving attacks and can therefore reduce the costs incurred by signalling. Using a novel theoretical model, we show that aposematic signals can indeed function as handicaps. To generate this prediction, we make a key assumption that the expression of bright displays and the storage of anti-predator toxins compete for resources within prey individuals. One shared currency is energy. However, competition for antioxidant molecules, which serve dual roles as pigments and in protecting prey against oxidative stress when they accumulate toxins, provides a specific candidate resource that could explain signal honesty. Thus, contrary to the prevailing theoretical orthodoxy, warning displays may in fact be honest signals of the level of (rather than simply the existence of) toxicity.