  Gauge theories with confining phases at low temperatures tend to deconfine at
high temperatures. In some cases, for example in supersymmetric theories,
confinement can persist for all temperatures provided the partition function
includes a grading by $(-1)^F$. When it is possible to define partition
functions which smoothly interpolate between no grading and $(-1)^F$ grading,
it is natural to ask if there are other choices of grading that have the same
effect as $(-1)^F$ on confinement. We explore how this works for
$\mathcal{N}=4$ SYM on $S^1\times S^3$ in the large $N$ limit at both small and
large coupling. We find evidence for a continuous range of grading parameters
that preserve confinement for all temperatures at large coupling, while at
small coupling only a discrete set of gradings preserves confinement.
