We show that systems of second-order ordinary differential equations, , subject to compatible nonlinear boundary conditions and impulses, have a solution x such that lies in an admissible bounding subset of when f satisfies a Hartman-Nagumo growth bound with respect to . We reformulate the problem as a system of nonlinear equations and apply Leray-Schauder degree theory. We compute the degree by homotopying to a new system of nonlinear equations based on the simpler system of ordinary differential equations, , subject to Picard boundary conditions and impulses and using the Leray index theorem. Our proof is simpler than earlier existence proofs involving nonlinear boundary conditions without impulses and requires weak assumptions on f. MSC:34A37, 34A34, 34B15.