In 1968, Louis de Brange studied the question, for what separated sequences ${a_i}$ on $R$ do there exist meromorphic inner functions on the upper half plane, whose spectrum is exactly the set ${a_i}$ and whose derivative is uniformly bounded on $\R$?. This long standing question was later revived by Anton Baranov in 2011. We will introduce and use the tools of Clark measures to characterize solutions of this problem.