  We take a modified boundary condition at the dead end of a stub to simulate
transmission zeroes being replaced by minima and then the discontinuous phase
slip (or decrease) at the transmission zeroes are replaced by a continuous but
rapid phase slip. The modified boundary condition can be continuously tuned to
give the results of the stub with hard wall boundary condition at the dead end
of stub. Even when the phase slip is continuous one can obtain information
about the density of states in the stub region from the scattering phases.
