  We investigate the infinite discontinuity points of stability diagram in
thin-shell wormholes. The square of the speed of sound $\beta _{0}^{2}$,\ which
is expressed in terms of pressure and energy density at equilibrium on the
throat, arises with a divergent amplitude. As this is physically
non-acceptable, \ we revise the equation of state, such that by fine-tuning of
the pressure at static equilibrium, which is at our disposal, eliminates such a
singularity. The efficacy of the method is shown in Schwarzschild, extremal
Reissner-Nordstr\"{o}m, and dilaton thin-shell wormholes.
