We consider Sturm-Liouville boundary-value problems on the interval [0, 1] of the form −y + qy = λy with boundary conditions y (0) sin α = y(0) cos α and y (1) = (aλ + b)y(1), where a < 0. We show that via multiple Crum-Darboux transformations, this boundary-value problem can be transformed 'almost' isospectrally to a boundary-value problem of the same form, but with the boundary condition at x = 1 replaced by y (1) sin β = y(1) cos β, for some β.