  We show that connections between a degree of incompatibility of pairs of
observables and the strength of violations of Bell's inequality found in recent
investigations can be extended to a general class of probabilistic physical
models. It turns out that the property of universal uniform steering is
sufficient for the saturation of a generalised Tsirelson bound, corresponding
to maximal violations of Bell's inequality. It is also found that a limited
form of steering is still available and sufficient for such saturation in some
state spaces where universal uniform steering is not given. The techniques
developed here are applied to the class of regular polygon state spaces, giving
a strengthening of known results. However, we also find indications that the
link between incompatibility and Bell violation may be more complex than
originally envisaged.
