Using a method introduced previously measurements were made of the $\ensuremath{\gamma}$-ray multiplicity ${N}_{\ensuremath{\gamma}}$ (the average number of $\ensuremath{\gamma}$ rays emitted in the decay of residual nuclei left by nuclear reactions) as a function of excitation energy ${E}^{*}$ for ($p,\ensuremath{\alpha}$) and ($d,\ensuremath{\alpha}$) reactions on $^{51}\mathrm{V}$, $^{56}\mathrm{Fe}$, and $^{57}\mathrm{Fe}$ targets; ($\ensuremath{\alpha},p$) reactions on $^{51}\mathrm{V}$, $^{56}\mathrm{Fe}$, $^{57}\mathrm{Fe}$, $^{58}\mathrm{Ni}$, $^{64}\mathrm{Ni}$, $^{93}\mathrm{Nb}$, and Ag; ($\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}}$) reactions on $^{51}\mathrm{V}$, $^{55}\mathrm{Mn}$, $^{56}\mathrm{Fe}$, $^{57}\mathrm{Fe}$, $^{59}\mathrm{Co}$, and $^{64}\mathrm{Ni}$; ($d,p$) reactions on $^{51}\mathrm{V}$, $^{55}\mathrm{Mn}$, $^{56}\mathrm{Fe}$, Ag, and $^{119}\mathrm{Sn}$; and ($p,{p}^{\ensuremath{'}}$) reactions on $^{56}\mathrm{Fe}$, $^{112}\mathrm{Sn}$, and $^{122}\mathrm{Sn}$. Bombarding energies ranged from 12 to 19 MeV. ${N}_{\ensuremath{\gamma}}$ was observed to be generally between 1 and 5 for ${E}^{*}$ between 3 and 10 MeV for the ($p,{p}^{\ensuremath{'}}$), ($d,p$), ($d,\ensuremath{\alpha}$), ($p,\ensuremath{\alpha}$), and ($\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}}$) reactions investigated, and somewhat higher for the ($\ensuremath{\alpha},p$) reactions. ${N}_{\ensuremath{\gamma}}$ increases with ${E}^{*}$, and is larger for higher angular momentum transfer reactions although it is not as much larger as angular momentum transfer considerations alone would suggest. (This can be explained as a level-density effect for compound-nucleus reactions---the average angular momentum of the states excited by the reactions is severely limited by the level-density spin-cutoff parameter.) The dependence of ${N}_{\ensuremath{\gamma}}$ on the average excess angular momentum of the residual nuclei was investigated using calculated spin distributions for the residual nuclei. This dependence is similar to that for neutron capture ${N}_{\ensuremath{\gamma}}'\mathrm{s}\ensuremath{-}{N}_{\ensuremath{\gamma}}$ increases with excess angular momenta for excess angular momenta of more than 2 or 3 units.