  Given a field $F$, a positive integer $m$ and an integer $n\geq 2$, we prove
that the symbol length of classes in Milnor's $K$-groups $K_n F/2^m K_n F$ that
are equivalent to single symbols under the embedding into $K_n F/2^{m+1} K_n F$
is at most $2^{n-1}$ under the assumption that $F \supseteq \mu_{2^{m+1}}$.
Since for $n=2$, $K_2 F/2^m K_2 F \cong {_{2^m}Br(F)}$, this coincides with the
upper bound of $2$ for the symbol length of central simple algebras of exponent
$2^m$ that are Brauer equivalent to a single symbol algebra of degree $2^{m+1}$
proved by Tignol in 1983. We also consider the cases where the embedding into
$K_n F/2^{m+1} K_n F$ is of symbol length 2, 3 and 4 (the latter when $n=2$).
We finish with studying the symbol length of classes in $K_3/3^m K_3 F$ whose
embedding into $K_3 F/3^{m+1} K_3 F$ is one symbol when $F \supseteq
\mu_{3^{m+1}}$.
