Compound-nuclear reactions induced by bombardment of $^{24}\mathrm{Mg}$, $^{26}\mathrm{Mg}$, and $^{27}\mathrm{Al}$ targets with 20-60-MeV $^{16}\mathrm{O}$, $^{18}\mathrm{O}$, and $^{19}\mathrm{F}$ beams have been used to study $\ensuremath{\gamma}$ transitions between high-spin states in nuclei in the mass region $32<~A<~44$. Results for $^{41}\mathrm{K}$ and $^{41}\mathrm{Ca}$ are presented to exemplify the method and results. The $\ensuremath{\gamma}$-ray decay of states with probable spins up to $\frac{19}{2}$ are observed in both nuclei.