  Information Causality is a physical principle which states that the amount of
randomly accessible data over a classical communication channel cannot exceed
its capacity, even if the sender and the receiver have access to a source of
nonlocal correlations. This principle can be used to bound the nonlocality of
quantum mechanics without resorting to its full formalism, with a notable
example of reproducing the Tsirelson's bound of the Clauser-Horne-Shimony-Holt
inequality. Despite being promising, the latter result found little
generalization to other Bell inequalities because of the limitations imposed by
the process of concatenation, in which several nonsignaling resources are put
together to produce tighter bounds. In this work, we show that concatenation
can be successfully replaced by limits on the communication channel capacity.
It allows us to re-derive and, in some cases, significantly improve all the
previously known results in a simpler manner and apply the Information
Causality principle to previously unapproachable Bell scenarios.
