The $\ensuremath{\gamma}$-to-charge multiplicity ratio $\frac{〈{M}_{\ensuremath{\gamma}}〉}{〈{M}_{\mathrm{ch}}〉}$ in $\overline{N}N$ annihilations is restricted by $I$-spin conservation. In deuterium, the ratio is constrained by $I$-spin conservation to be equal to 1, while an experiment reported a value of 1.24\ifmmode\pm\else\textpm\fi{}0.03; this measurement was based on missing and $\ensuremath{\gamma}$ energies. The experiment reported in this paper measures the rate of conversion of $\ensuremath{\gamma}'\mathrm{s}$ as a function of converter thickness and obtains $\frac{〈{M}_{\ensuremath{\gamma}}〉}{〈{M}_{\mathrm{ch}}〉}=1.26\ifmmode\pm\else\textpm\fi{}0.03$ for $\overline{p}p$ annihilations, which is in agreement with the large $\ensuremath{\gamma}$ excess observed in deuterium. Statistical models which ignore $I$-spin conservation predict such a $\ensuremath{\gamma}$ excess, while those taking into account $I$-spin conservation predict values near 1.