Let
G
G
be a connected reductive group over a finite field
f
\mathfrak {f}
of order
q
q
. When
q
≤
5
q\leq 5
, we make further assumptions on
G
G
. Then we determine precisely when
G
(
f
)
G(\mathfrak {f})
admits irreducible, cuspidal representations that are self-dual, of Deligne-Lusztig type, or both. Finally, we outline some consequences for the existence of self-dual supercuspidal representations of reductive
p
p
-adic groups.