Summary: New integrable boundary conditions for integrable quantum systems can be constructed by tuning of scattering phases due to reflection at a boundary and an adjacent impurity and subsequent projection onto subspaces. We illustrate this mechanism by considering a \(gl(m< n)\)-impurity attached to an open \(gl(n)\)-invariant quantum chain and a Kondo spin \(S\) coupled to the supersymmetric \(t\)-\(J\) model.