Recent efforts to reduce international tax evasion focus on information exchange with tax havens. Using bilateral bank data for 1397 countrypairs in a balanced quarterly panel from 2003:I to 2017:IV, we first show that information-on-request treaties with tax havens reduce bank deposits in tax havens by 27.5%. Second, also deposits from tax havens in high tax countries decline after such treaties are signed, giving authorities a second angle to detect tax evasion. Both reactions dissipate overt time and treaties signed after 2010 trigger no further reactions. These results cannot be explained by deposit shifting alone and we find no evidence of transitioning into legality. Third, recent policy initiatives based on the automatic exchange of bank information lead to very similar initial reactions as earlier treaties, consistent with adjustments on the part of tax evaders. This suggests that tax evaders adapt to established information exchange treaties by using new disguises to hide their true income, and react again to new measures. These results cast doubt on the effectiveness of current forms of information exchange to tackle international tax evasion.