How can the lack of reaction of aggregate exports to Real Exchange Rate (RER) volatility be explained? Using a French firm-level database that combines balance-sheet and product-destination-specific export information over the period 1995-2009, we propose a micro-founded explanation to this macro puzzle, by investigating how firms reallocate exports across destinations following RER volatility shocks. We show that firm-level bilateral exports to a considered destination also react to external volatility, represented by several indicators we build. Firms tend to reallocate exports away from destinations with unfavorable dynamics in terms of RER volatility, and this effect grows with the scope of possible reallocations. Efficient diversification of destinations served appear therefore as another way to handle exchange rate risks, and provides an explanation to the small aggregate trade response to RER volatility: if big multi-destination firms, who account for the bulk of aggregate exports, can react to an adverse shock of RER volatility somewhere by transferring trade to other and less volatile destinations, this leaves exports mainly unchanged at the macro level.