let $k$ be a compact lie group and $v$ a unitary $k$-module. let $\mu\colon v\to \frak k^*$ be the associated moment mapping and let $m_0$ denote the quotient of $\mu^{-1}(0)$ by $k$. this is the (symplectic) quotient associated to the $k$-action. now $k$ is a real algebraic subgroup of the unitary group of $v$ and its complex points are a complex reductive subgroup $g$ of $\rm{gl}(v)$. we recall the invariant theory quotient $v{/\!\!/} g$ associated to the $g$-action, and the fact that $v{/\!\!/} g$ is homeomorphic to $m_0$. this fact is enormously useful. the simplest kinds of symplectic quotients are those of the form $w/h$ where $w$ is a unitary $h$-module and $h$ is finite. let $\dim k>0$. for $k$-modules $v$ which are ``small,'' there are examples of isomorphisms of $m_0$ with some $w/h$. we show that for most $k$-modules, there can be no such isomorphism. we give necessary and sufficient conditions for such isomorphisms for $k=s^1$ and $k=\rm{su}(2,\bbb c)$. this is joint work with h.-c. herbig and c. seaton.