The objective of this paper is to analyze the external sector on Cuban tobacco from the export demand perspective towards the euro area. A tobacco-specific exchange rate is built to better capture the distinctions of this sector when competing overseas. We apply cointegration in the Fully-Modified Ordinary Least Squares framework and complement an error correction mechanism. It is found that both long and short-run estimates of exchange rate elasticities are significantly inelastic but present, at the same time, a high degree of stability. This means that prices become a fundamental control variable for economic policy purposes. Moreover, there is statistical evidence that income elasticity plays a significant role in the determination of exports growth for Cuban tobacco.