  We prove an upper bound on the sum of the distances between the eigenvalues
of a perturbed Schr\"odinger operator $H_0-V$ and the lowest eigenvalue of
$H_0$. Our results hold for operators $H_0=-\Delta-V_0$ in one dimension with
single-well potentials. We rely on a variation of the well-known commutation
method. In the P\"oschl-Teller and Coulomb cases we are able to use the
explicit factorisations to establish improved bounds.
