This study combines block-recursive restrictions with higher-order moment conditions to identify and estimate non-Gaussian structural vector autoregressions. The estimator allows to impose a block-recursive structure on the SVAR and for a given block-recursive structure we derive a conservative set of assumptions on the dependence and Gaussianity of the shocks to ensure identification. We use a Monte Carlo simulation to illustrate the advantages of the proposed blockrecursive estimator compared to unrestricted, purely data driven estimators in small samples. The block-recursive estimator is used to analyze the interdependence of monetary policy and the stock market. We find that a positive stock market shock contemporaneously increases the nominal interest rate, while contractionary monetary policy shocks lead to lower stock returns on impact.