Putting a price on carbon is critical for climate change policy. Increasingly, policymakers combine multiple policy tools to achieve this, for example by complementing cap-and-trade schemes with a carbon tax, or with a feed-in tariff. Often, the motivation for doing so is to limit undesirable fluctuations in the carbon price, either from rising too high or falling too low. This paper reviews the implications for the carbon price of combining cap-and-trade with other policy instruments. We find that price intervention may not always have the desired effect. Simply adding a carbon tax to an existing cap-and-trade system reduces the carbon price in the market to such an extent that the overall price signal (tax plus carbon price) may remain unchanged. Generous feed-in tariffs or renewable energy obligations within a capped area have the same effect: they undermine the carbon price in the rest of the trading regime, likely increasing costs without reducing emissions. Policymakers wishing to support carbon prices should turn to hybrid instruments — that is, trading schemes with price-like features, such as an auction reserve price — to make sure their objectives are met.