  We introduce and study a new class of integral domains which we call
irreducible divisor pair domains (IDPDs). In particular, we show how IDPDs fit
in with other classes of integral domains defined in terms of factorization
conditions. For instance, every UFD is an IDPD, and every IDPD is an HFD, but
the converses fail in general. We also show that many familiar examples of HFDs
are also IDPDs.
