  We consider the following singularly perturbed Neumann problem {eqnarray*}
\ve^2 \Delta u -u +u^p = 0 \quad {{in}} \quad \Omega, \quad u>0 \quad {{in}}
\quad \Omega, \quad {\partial u \over \partial \nu}=0 \quad {{on}} \quad
\partial \Omega, {eqnarray*} where $p$ is subcritical and $\Omega$ is a smooth
and bounded domain in $\R^n$ with its unit outward normal $\nu$. Lin-Ni-Wei
\cite{LNW} proved that there exists $\ve_0$ such that for $0<\ve<\ve_0$ and for
each integer $k$ bounded by {equation} 1\leq k\leq
\frac{\delta(\Omega,n,p)}{(\ve |\log \ve |)^n} {equation} where
$\delta(\Omega,n,p)$ is a constant depending only on $\Omega$, $p$ and $n$,
there exists a solution with $k$ interior spikes. We show that the bound on $k$
can be improved to {equation} 1\leq k\leq \frac{\delta(\Omega,n,p)}{\ve^n},
{equation} which is optimal.
