New supersymmetric (SUSY) partners of the modified Poschl-Teller and the Di
rac's delta well potentials are constructed in closed form. The resulting o
ne-parametric potentials are shown to be interrelated by a limiting process
. The range of values of the parameters for which these potentials are free
of singularities is exactly determined. The construction of higher-order S
USY partner potentials is also investigated.