We prove that the general symmetric tensor in
S
d
C
n
+
1
S^d\mathbb {C}^{n+1}
of rank
r
r
is identifiable, provided that
r
r
is smaller than the generic rank. That is, its Waring decomposition as a sum of
r
r
powers of linear forms is unique. Only three exceptional cases arise, all of which were known in the literature. Our original contribution regards the case of cubics (
d
=
3
d=3
), while for
d
≥
4
d\ge 4
we rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and Mella.