  Let the finite distributive lattice $D$ be isomorphic to the congruence
lattice of a finite lattice $L$. Let $Q$ denote those elements of $D$ that
correspond to principal congruences under this isomorphism. Then $Q$ contains
$0,1 \in D$ and all the join-irreducible elements of $D$. If $Q$ contains
exactly these elements, we say that $L$ is a minimal representations of $D$ by
principal congruences of the lattice $L$.
  We characterize finite distributive lattices $D$ with a minimal
representation by principal congruences with the property that $D$ has at most
two dual atoms.
