Stringent Technical Barriers to Trade (TBT) are expected to drive exporters out of the markets imposing these hurdles. However their impact will vary, with some exporters being able to refocus on TBT-free markets. By matching a database of TBT measures raised as concerns at the WTO (Specific Trade Concerns - STCs), with a firm-level panel of French exporters, we show the complex effects of restrictive TBT measures on the different margins of trade. We show that the negative effect of TBT on export participation is magnified for multi-destination firms, which can divert their exports towards TBT-free destinations. Moreover, we conduct aggregate level estimations to show that the effect of stringent TBTs in reducing export ows is magnified in more homogeneous sectors. Observing the shape of the firm distribution at sectoral level and the aggregate elasticity of export to trade cost, we shed light on the fixed component of the additional cost imposed by TBTs on exporters.