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We prove congruences for the number of partition pairs   $(\pi _1,\pi _2)$   such that   $\pi _1$   is non-empty,   $s(\pi _1)\le s(\pi _2)$   and   $\ell (\pi _2)\lt 2s(\pi _1)$  , where   $s(\pi )$   is the smallest part and   $\ell (\pi )$   is the largest part of a partition. The proofs use Bailey's Lemma and a generalized Lambert series identity of Chan. We also discuss how a partition pair crank gives combinatorial refinements of these congruences.

CONGRUENCES FOR PARTITION PAIRS WITH CONDITIONS