Fix a prime
p
p
and let
F
F
be a field with characteristic not
p
p
. Let
G
F
G_F
be the absolute Galois group of
F
F
, and let
μ
p
s
\mu _{p^s}
be the
G
F
G_F
-module of roots of unity of order dividing
p
s
p^s
in a fixed algebraic closure of
F
F
. Let
α
∈
H
n
(
F
,
μ
p
s
⊗
n
)
\alpha \in H^n(F,\mu _{p^s}^{\otimes n})
be a symbol (i.e.,
α
=
a
1
∪
⋯
∪
a
n
\alpha =a_1\cup \dots \cup a_n
where
a
i
∈
H
1
(
F
,
μ
p
s
)
a_i\in H^1(F, \mu _{p^s})
) with effective exponent dividing
p
s
−
1
p^{s-1}
(that is
p
s
−
1
α
=
0
∈
H
n
(
G
F
,
μ
p
⊗
n
)
p^{s-1}\alpha =0\in H^n(G_F,\mu _p^{\otimes n})
. In this work, we show how to write
α
\alpha
as a sum of symbols coming from
H
n
(
F
,
μ
p
s
−
1
⊗
n
)
H^n(F,\mu _{p^{s-1}}^{\otimes n})
, that is, symbols of the form
p
γ
p\gamma
for
γ
∈
H
n
(
F
,
μ
p
s
⊗
n
)
\gamma \in H^n(F,\mu _{p^s}^{\otimes n})
. If
n
>
3
n>3
and
p
≠
2
p\neq 2
, we assume
F
F
is prime to
p
p
closed and of characteristic zero. In the case
p
=
2
p=2
, we also bound the symbol length of a sum of two symbols with effective exponent dividing
p
s
−
1
p^{s-1}
.