  We use Arveson's notion of strongly peaking representation to generalize
uniqueness theorems for free spectrahedra and matrix convex sets which admit
minimal presentations. A fully compressed separable operator system necessarily
generates the C*-envelope and is such that the identity is the direct sum of
strongly peaking representations. In particular, a fully compressed
presentation of a separable operator system is unique up to unitary
equivalence. Under various additional assumptions, minimality conditions are
sufficient to determine a separable operator system uniquely.
