  An ideal I in a Noetherian ring R is normally torsion-free if
Ass(R/I^t)=Ass(R/I) for all natural numbers t. We develop a technique to
inductively study normally torsion-free square-free monomial ideals. In
particular, we show that if a square-free monomial ideal I is minimally not
normally torsion-free then the least power t such that I^t has embedded primes
is bigger than beta_1, where beta_1 is the monomial grade of I, which is equal
to the matching number of the hypergraph H(I) associated to I. If in addition I
fails to have the packing property, then embedded primes of I^t do occur when
t=beta_1 +1. As an application, we investigate how these results relate to a
conjecture of Conforti and Cornu\'ejols.
