  The famous Clauser-Horne-Shimony-Holt (CHSH) inequality certifies a quantum
violation, by a factor $\sqrt{2}$, of correlations predicted by the classical
view of the world in the simplest possible nontrivial measurement setup (two
systems with two dichotomic measurements each). In such setting, this is the
largest possible violation, which is known as the \emph{Tsirelson bound}. In
this paper we calculate the exact values of quantum violations for the other
Bell correlation inequalities that appear in the setups involving up to four
measurements; they are all smaller than $\sqrt{2}$. While various authors
investigated these inequalities via numerical methods, our approach is
analytic. We also include tables summarizing facial structure of Bell polytopes
in low dimensions.
