Past empirical research on monetary policy in open economies has found evidence of the 'delayed overshooting', the 'forward discount' and the 'exchange rate' puzzles. We revisit the effects of monetary policy on exchange rates by applying Uhlig's (2005) identification procedure that involves sign restrictions on the impulse responses of selected variables. We impose no restrictions on the exchange rate to leave the key question as open as possible. The sign restriction methodology avoids the price puzzles of the identification strategies used by Eichenbaum-Evans (1995) and by Grilli-Roubini (1995, 1996), which are particularly pronounced, when using an updated data set. We find that the puzzles regarding the exchange rates are still there, but that the quantitative features are different. In response to US monetary policy shocks, the peak appreciation happens during the first year after the shock for the US-German and the US-UK pair, and during the first two years for the US-Japan pair. This is consirably quicker than the three-year horizon found by Eichenbaum-Evans. There is a robust forward discount puzzle implying a large risk premium. We study this issue, introducing and calculating conditional Sharpe ratios for a Bayesian investor investing in a hedged position following a US monetary policy shock. For foreign monetary policy shocks, we find more robust results than with the Grilli-Roubini recursive identification strategy: the posterior distribution regarding the exchange reaction looks rather similar across countries and VAR specifications. In particular, we find that there seems to be considerable uncertainty regarding the initial reaction of the exchange rate. Quantitatively, monetary policy shocks seem to have a minor impact on exchange rate fluctuations.