  Given a nonempty finite multiset $S$ of positive integers, we wish to find a
partially ordered set $P$ of minimal cardinality such that the multiset of
cardinalities of all maximal chains in $P$ equals $S$. This paper establishes
upper and lower bounds on the size of $P$: $\max(S) + \lceil \log_2 |S| \rceil
<= |P| <= \max(S) + |S| - 1$, and both bounds are tight.
