Authors’ abstract: In the first part of this note, we give a rather short proof of a generalization of W. Stenger’s lemma [Bull. Am. Math. Soc. 74, 369–372 (1968; Zbl 0153.45105)] about the compression \(A_{0}\) to \(\mathfrak{H}_{0}\) of a self-adjoint operator \(A\) in some Hilbert space \(\mathfrak{H}=\mathfrak{H}_{0}\oplus \mathfrak{H}_{1}\). In this situation, \(S:=A\cap A_{0}\) is a symmetry in \(\mathfrak{H}_{0}\) with the canonical self-adjoint extension \(A_{0}\) and the self-adjoint extension \(A\) with exit into \(\mathfrak{H}\). In the second part, we consider relations between the resolvents of \(A\) and \(A_{0}\) like M. G. Krein’s resolvent formula, and corresponding operator models.