The well-known uncovered interest parity puzzle arises from the empirical regularity that, among developed country pairs, the high interest rate country tends to have high expected returns on its short term assets. At the same time, another strand of the literature has documented that high real interest rate countries tend to have currencies that are strong in real terms - indeed, stronger than can be accounted for by the path of expected real interest differentials under uncovered interest parity. These two strands - one concerning short-run expected changes and the other concerning the level of the real exchange rate - have apparently contradictory implications for the relationship of the foreign exchange risk premium and interest-rate differentials. This paper documents the puzzle, and shows that existing models appear unable to account for both empirical findings. The features of a model that might reconcile the findings are discussed.