Summary: We explore the possibilities for the Galois representation \(\rho_g\) attached to a weight-one newform \(g\) to be residually reducible, i.e. for the Hecke eigenvalues to be congruent to those of a weight-one Eisenstein series. A special role is played by Eisenstein series \(E_1^{1, \eta_K}\) of level \(d_K\), where \(\eta_K\) is the quadratic character associated with an imaginary quadratic field \(K\), of discriminant \(d_K\), with respect to which \(\rho_g\) is of dihedral type. We prove congruences, where the modulus divides either the class number \(h_K\) or \((p- \eta_K(p))\) (for a prime \(p)\), and \(g\) is of level \(d_K\) in the first case, level \(d_Kp\) or \(d_K p^2\) (according as \(\eta_K(p)=1\) or \(-1,\) respectively) in the second. We also prove analogous congruences where \(1\) and \(\eta_K\) are replaced by a newform \(f\) and its twist by \(\eta_K\), and \(g\) is replaced by a Siegel cusp form of genus \(2\) and paramodular level, induced in some sense from a Hilbert modular form.