  The cusped hyperbolic n-orbifolds of minimal volume are well known for $n
\leq 9$. Their fundamental groups are related to the Coxeter n-simplex groups
$\Gamma_n$ listed in Table 1. In this work, we prove that $\Gamma_n$ has
minimal growth rate among all non-cocompact Coxeter groups of finite covolume
in $\hbox{Isom}\mathbb H^n$. In this way, we extend previous results of Floyd
for $n = 2$ and of Kellerhals for $n = 3$ respectively. Our proof is a
generalisation of the methods developed in [2] for the cocompact case.
