The value of preferential market access schemes has fallen sharply. Drawing on a relaxation announcement of July 2016 simplifying origin requirements for access to the EU that should help improve market access, thereby contributing to alleviate the refugee crisis in Jordan, this paper argues that a simplification of origin requirements is a straightforward way to enhance preferential market access. Yet, the EU decision limits the beneficiaries who must be located in designated special economic zones, which limits preferential market access. The paper compares the performance of Jordanian exports to the EU and the US under their respective FTAs. It shows that Jordanian exports to the US have grown more rapidly than exports to the EU over the last 15 years. The study documents lower utilisation of preferences in the EU than in the US, especially in Textiles and Apparel (T&A) in spite of non-negligible preferences. Three contributing factors are identified: (i) higher adjusted preferences for apparel in the US than in the EU; (ii) greater competition from other suppliers (mostly from LDCs) in the EU market than in the US market; (iii) simpler origin requirements in the case of the Jordan–US FTA. Comparative evidence from the two FTAs and econometric estimates suggest that this should help restore market access for Jordanian exports to the EU. These estimates provide additional evidence that origin requirements suppress market access. Other pathways to simplify origin requirements are offered in the conclusion.