The ability of diagrams to convey information effectively in part comes from their ability to make facts explicit that would otherwise need to be inferred. This type of advantage has often been referred to as a free ride and was deemed to occur only when a diagram was obtained by translating a symbolic representation of information. Recent work gen- eralised free rides to the idea of an observational advantage, where the existence of such a translation is not required. Roughly speaking, it has been shown that Euler diagrams without existential import are observa- tionally complete as compared to symbolic set theory. In this paper, we explore to what extent Euler diagrams with existential import are ob- servationally complete with respect to set-theoretic sentences. We show that existential import significantly limits the cases when observational completeness arises, due to the potential for overspecificity.