  Event isotropy $\mathcal{I}^\text{sph}$, an event shape observable that
measures the distance of a final state from a spherically symmetric state, is
designed for new physics signals that are far from QCD-like. Using a new
technique for producing a wide variety of signals that can range from
near-spherical to jetty, we compare event isotropy to other observables. We
show that thrust $T$ and the $C$ parameter (and $\lambda_\text{max}$, the
largest eigenvalue of the sphericity matrix) are strongly correlated and thus
redundant, to a good approximation. By contrast, event isotropy adds
considerable information, often serving to break degeneracies between signals
that would have almost identical $T$ and $C$ distributions. Signals with broad
distributions in $T$ (or $\lambda_\text{max}$) and in $\mathcal{I}^\text{sph}$
separately often have much narrower distributions, and are more easily
distinguished, in the $({\mathcal{I}^\text{sph}},\lambda_\text{max})$ plane. An
intuitive, semi-analytic estimation technique clarifies why this is the case
and assists with the interpretation of the distributions.
