Spain is a paradox of European cohesion policy. One of the EU's largest historical recipients of Structural and Investment Funds, it has nonetheless diverged from (rather than converged toward) the EU average. Why do substantial transfers fail to produce convergence? This paper argues that neither funding volumes nor institutional quality, two factors commonly emphasised in the literature, can on their own explain regional trajectories. Instead, we identify political stability and strategic capability-building as individually necessary but insufficient conditions that become sufficient only in combination: convergence occurs when regions combine durable political stability with a deliberate channelling of cohesion funds toward human capital formation, productive investment, and private sector mobilisation. Our empirical strategy is twofold. We first test our argument through a cross-regional quantitative analysis of Spain's seventeen autonomous communities (2000–2023), which we then complement with a structured comparison of Galicia and Andalucía. Both regions ranked very similarly on all of our variables in the early 2000s but have ever since diverged, with Andalucía becoming the poorest region and Galicia comfortably sitting in the Spanish regional ‘middle-class’. Drawing on elite interviews, policy mapping, and an analysis of cohesion fund projects, we trace how Galicia's performance reflects the joint presence of both conditions, a combination absent in the Andalusian case.