From a study of 15-GeV/c ${\pi }^{+}$-deuterium interactions obtained in an 890 000-picture exposure in the SLAC 82-inch bubble chamber, evidence is presented for at least two broad dipion states beyond the $g\left(1680\right)\mathrm{}$ region. These states appear in the spectrum representing highly peripheral interactions, and in the spectra obtained by eliminating those interactions for which the transverse momentum of each pion is less than a specified minimum value. Further, examination of the ${\pi }^{+}{\pi }^{-}\mathrm{MM}$ (missing mass) spectrum from the reaction ${\pi }^{+}n\to p{\pi }^{+}{\pi }^{-}\left(\mathrm{MM}\right)$ indicates that agreement with the previously obtained branching ratios is possible only if higher-mass dipion states are present. Evidence is also presented which suggests a finite decay probability of the $g$ (or a state of similar mass) into ${\pi }^{+}{\pi }^{-}\eta$ and/or ${\pi }^{+}{\pi }^{-}{\eta }^{\prime }$.

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