We estimate structurally a model of the term structure of interest rates that is consistent with no arbitrage but allows for demand pressures. The term structure in our model is determined through the interaction of risk-averse arbitrageurs and preferred-habitat investors with preferences for specific maturities. The model is estimated on US real rates during the 2000s and allows for two factors: one corresponding to the short rate and one to preferred-habitat demand. We find that the puzzling drop in long rates during 2004-05 (Greenspan conundrum) is driven by the demand factor. International reserves, foreign official holdings of longer-term US Treasuries may all be proxies for the preferred-habitat demand factor. For example, foreign purchases in the year to July 2004 appear to have lowered the ten-year rate by about 100 basis points. Foreign purchases have larger effects following periods when arbitrageurs have lost money.