Many governments aim to reduce the dependence on coal-fired generation to decrease carbon emissions. At the same time power markets with competition between independently operating power firms have been created which leave the actual decisions concerning electricity production to these firms. This paper analyzes the interaction between climate policies and policies to foster power markets. Using hourly plant-level data on the Dutch power market over 2006-2014, we find that the dispatch of fossil-fuel power plants is strongly influenced by relative fuel prices, despite the existence of several climate policy measures. Coal-fired power plants have become more important in the Dutch market since 2006, not only in share of total production, but also as provider of flexibility. Examining the short-term dispatch decisions and the past volatility in relative fuel prices, the maximum CO2 price which was needed to provide incentives for power producers to dispatch a gas-fired plant instead of a coal-fired plant was 43 euro/ton. We conclude that internalizing the external (CO2) costs by raising the CO2 price is a more appropriate measure than a forced closure of coal-fired power plants to align the principles of a market-based power industry and the wish to implement effective climate-policy measures at relatively low costs.