Portugal’s post-1960 growth was export-led, but the economy is now in the doldrums: GDP per capita has plateaued at roughly two-thirds of the EU average and merchandise export growth has slowed to its weakest sustained rate in six decades. Using an illustrative quality-threshold trade model, with non-homothetic demand and capability dependent costs, we show how an intermediate-capability country such as Portugal can fall into what we describe as an European market-concentration trap. The empirical record, covering six phases of Portuguese trade history from 1960, is consistent with this model. As a remedy, we propose that the country should revive exports as an engine of growth by diversifying their geographic destination, in particular to countries in the Global South. Applying an export Decision-Support Model (DSM) to CEPII-BACI trade data, we estimate significant untapped short-term export potential (around euro billion) for Portugal across a combination of 16 products to 8 markets in the Global South. Diversifying exports to markets where Portugal’s existing capability is a comparative advantage may generate revenue, scale and firm-level learning which would promote the country’s technological upgrading.