This paper gives new insights about flight-to-safety from stocks to bonds, asking whether the strength of this phenomenon remains the same in the current environment of low yields. The motivations lie on the conjecture that when yields are low, the traditional motives of flight-to-safety (wealth protection, liquidity) could not be sufficient, inducing weaker flight-to-safety events. Empirical applications using data for US government bonds and the S&P 500 index, show indeed that when yields are low, the strength of flight-to-safety from stocks to bonds weakens. Moreover, we develop a bivariate model of flight-to-safety transfers that measures to what extent the strength of flight-to-safety from stocks to bonds is related to the strength of flight-to-safety from stocks to other safe haven assets (gold and currencies). Results show that when the strength of flight-to-safety from stocks to bonds decreases the strength of flight-to-safety from stocks to gold increases. This result holds only in the current low-yield environment, suggesting a shift in the historical attractiveness of bonds as safe haven.