  We show that if a noncollapsed $CD(K,n)$ space $X$ with $n\ge 2$ has
curvature bounded above by $\kappa$ in the sense of Alexandrov then $K\le
(n-1)\kappa$ and $X$ is an Alexandrov space of curvature bounded below by
$K-\kappa (n-2)$. We also show that if a $CD(K,n)$ space $Y$ with finite $n$
has curvature bounded above then it is infinitesimally Hilbertian.
