This paper investigates a trade model with many countries, many goods produced in multiple quality versions and non-homothetic preferences. It studies the impact of productivity, population changes and trade costs on the quality composition of exports. The analysis embeds within the same model a series of empirical results about high-income countries' specialisation and trade in higher quality goods. Product differentiation matters at explaining the volumes of trade quality. High-quality goods exhibing a high degree of differentiation are traded only by high-income countries.