  The aim of this paper is to obtain a uniform bound for a certain class of
submodules from the following theorem: Let $(R,\frak m)$ be a local ring, let
$M$ be a finite $R$--module of dimension $d\ge 1$ and let $\frak q$ be an ideal
of $R$ generated by a system of parameters on $M$. Let $N$ be a submodule of
$M$ with $\depth M/N\ge d-1$. Then $\ell(N/\frak qN)\le\ell(M/\frak qM)$.
