Since the pioneering work of Tinbergen (1962) and Pöyhonen (1963), the gravity model has become the standard tool to study bilateral trade. Alternative approaches, such as a complete demand system by country as in Barten et al. (1976), were never very popular. We propose several extensions of the standard gravity model. The modified equation is tested using panel data of 140 observations over the period 2000-2008. This yields a specification that allows for (i) a more flexible income response; (ii) a competitiveness effect with a general and a specific component; and (iii) an alternative and consistent measure of remoteness. The extensions were found to be significant factors in explaining intra-EU trade.