  Non-signalling boxes (NS) are theoretical resources defined by the principle
of no-faster-than-light communication. They generalize quantum correlations,
and some of them are known to collapse communication complexity (CC). However,
this collapse is strongly believed to be unachievable in Nature, so its study
provides intuition on which theories are unrealistic. In the present letter, we
find a better sufficient condition for a nonlocal box to collapse CC, thus
extending the known collapsing region. In some slices of NS, we show this
condition coincides with an area outside of an ellipse.
