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We show that the introduction of Tobin taxes in agent-based models of currency markets can lead to a reduction of both speculative trading and the magnitude of exchange rate fluctuations at intermediate tax rates. In this regime revenues obtained from speculators are maximal for the institutions acting as market makers. We here focus on minority game models of markets, which are accessible by exact techniques from statistical mechanics. Results are supported by computer simulations. Our findings suggest that at finite systems sizes the effect is most pronounced in a critical region around the phase transition of the infinite system, but much weaker if the market is operating far from criticality and does not exhibit anomalous fluctuations.