  A zero-sum sequence over ${\mathbb Z}$ is a sequence with terms in ${\mathbb
Z}$ that sum to $0$. It is called minimal if it does not contain a proper
zero-sum subsequence. Consider a minimal zero-sum sequence over ${\mathbb Z}$
with positive terms $a_1,\ldots,a_h$ and negative terms $b_1,\ldots,b_k$. We
prove that $h\leq \lfloor \sigma^+/k\rfloor$ and $k\leq \lfloor
\sigma^+/h\rfloor$, where $\sigma^+=\sum_{i=1}^h a_i=-\sum_{j=1}^k b_j$. These
bounds are tight and improve upon previous results. We also show a natural
partial order structure on the collection of all minimal zero-sum sequences
over the set $\{i\in {\mathbb Z}:\; -n\leq i\leq n\}$ for any positive integer
$n$.
