  We derive new tight bipartite Bell inequalities for various scenarios. A
bipartite Bell scenario $(X,Y,A,B)$ is defined by the numbers of settings and
outcomes per party, $X$, $A$ and $Y$, $B$ for Alice and Bob, respectively. We
derive the complete set of facets of the local polytopes of $(6,3,2,2)$,
$(3,3,3,2)$, $(3,2,3,3)$, and $(2,2,3,5)$. We provide extensive lists of facets
for $(2,2,4,4)$, $(3,3,4,2)$ and $(4,3,3,2)$. For each inequality we compute
the maximum quantum violation, the resistance to noise, and the minimal
symmetric detection efficiency required to close the detection loophole, for
qubits, qutrits and ququarts. Based on these results, we identify scenarios
which perform better in terms of visibility, resistance to noise, or both, when
compared to CHSH. Such scenarios could find important applications in quantum
communication.
