  We investigate the homotopy groups of the configuration space of hard discs
inside a unit disc, just beyond the first critical radius. In the four-disc
case, we find a non-contractible `thick braid' (loop in the configuration
space), which contracts in the ordered configuration space of points when we
replace each disc by its centre. For $n\ge 5$ discs, we find a non-contractible
$(n-3)$-sphere, and we explore the persistence of this homotopy class when the
ambient unit disc is deformed. For sufficiently large $n$, we demonstrate the
existence of non-trivial $\pi_k$-classes with $k<n-3$ beyond higher critical
radii.
