Let $M$ be a compact smooth orientable CR hypersurface of CR dimension $m$, equipped with a smooth density and Hermitian metric on tangential forms. Fix a degree $q$ with $0\le q\le m$, and suppose that $M$ satisfies Kohn's condition $Y(q)$ at every point. At the endpoints this hypothesis is interpreted literally: for instance, in the positive strictly pseudoconvex orientation it applies to $q=m$ but not to $q=0$. Then the closed $L^2$ realisations of $\bar\partial_b$ and $\bar\partial_b^*$ at degree $q$ satisfy a subelliptic estimate: there exist constants $\varepsilon>0$ and $C>0$ such that \begin{align*} \|u\|_{H^\varepsilon(M,\Lambda_b^{0,q}M)}^2 \le C\bigl(\|\bar\partial_bu\|_{L^2}^2+\|\bar\partial_b^*u\|_{L^2}^2+\|u\|_{L^2}^2\bigr) \end{align*} for every smooth tangential $(0,q)$-form $u$ lying in the relevant operator domains. When $q=0$, the term $\bar\partial_b^*u$ is omitted; when $q=m$, the term $\bar\partial_bu$ is omitted.