For a non-flat
C
3
C^3
unimodal map with a Cantor attractor, we show that for any open cover
U
\mathcal U
of this attractor, the complexity function
p
(
U
,
n
)
p(\mathcal U, n)
is of order
n
log
n
n\log n
. In the appendix, we construct a non-renormalizable map with a Cantor attractor for which
p
(
U
,
n
)
p(\mathcal {U}, n)
is bounded from above for any open cover
U
\mathcal {U}
.