  Let $R$ be a Noetherian local ring and let $I$ be an ideal in $R$. The ideal
$I$ is called balanced if the colon ideal $J:I$ is independent of the choice of
the minimal reduction $J$ of $I$. Under suitable assumptions, Ulrich showed
that $I$ is balanced if and only if the reduction number, $r(I)$, of $I$ is at
most the `expected' one, namely $\ell(I)- \height I+1$, where $\ell(I)$ is the
analytic spread of $I$. In this article we propose a generalization of
balanced. We prove under suitable assumptions that if either $R$ is
one-dimensional or the associated graded ring of $I$ is Cohen-Macaulay, then
$J^{n+1}:I^n$ is independent of the choice of the minimal reduction $J$ of $I$
if and only if $r(I) \leq \ell(I)-\height I+n$.
