  Conjecture A of \cite{EM14} predicts the equality between the smallest
positive height of the irreducible characters in a $p$-block of a finite group
and the smallest positive height of the irreducible characters in its defect
group. Hence, it can be seen as a generalization of Brauer's famous height zero
conjecture. One inequality was shown to be a consequence of Dade's Projective
Conjecture. We prove the other, less well understood, inequality for principal
blocks when the defect group has two character degrees.
