Smart specialization has become a hallmark of the EU's Cohesion Policy. Envisaged as a bottom-up initiative identifying local knowledge cores and associated competitive advantages, the operationalization of smart specialization has been rather limited, as a coherent set of analytical tools to guide the policy directives remains elusive. To tackle the weak underpinning of smart specialization policy, we propose a policy framework around the concepts of relatedness and knowledge complexity. We use EPO patent data to provide evidence on how EU regions develop new technologies in the period 1990-2009. We find that diversifying into more complex technologies is highly attractive but difficult for EU regions to accomplish. Regions can overcome this diversification dilemma by developing new complex technologies that build on local related capabilities. We use these findings to construct a policy framework for smart specialization that highlights the potential risks and rewards for regions of adopting competing diversification strategies. We show how potential costs of alternative strategies in regions may be assessed by making use of the relatedness concept, and how potential benefits of various smart specialization strategies can be derived from estimates of the complexity of technologies. A series of case-studies of different types of regions illustrate the utility of this policy framework.