  Let $K$ be a null-homologous knot in a generalized L-space $Z$ with
$b_1(Z)\le1$. Let $F$ be a Seifert surface of $K$ with genus $g$. We show that
if $\widehat{HFK}(Z,K,[F],g)$ is supported in a single $\mathbb Z/2\mathbb
Z$--grading, then
\[\mathrm{rank}\widehat{HFK}(Z,K,[F],g-1)\ge\mathrm{rank}\widehat{HFK}(Z,K,[F],g).\]
