The neutron-deficient Ca isotopes continue to attract attention due to their importance for testing isospin symmetry and their relevance in capture reactions of interest for nova nucleosynthesis and the shape of light curves in Type I x-ray bursts. To date, spectroscopic information on $^{38,39}\mathrm{Ca}$ is largely limited to data on lower-spin excited states. Here, we report in-beam $\ensuremath{\gamma}$-ray spectroscopy of complementary higher-spin, complex-structure states in $^{39}\mathrm{Ca}$ populated in fast-beam-induced, momentum-dissipative processes leading to neutron pickup onto excited configurations of the projectile, $^{9}\mathrm{Be}(^{38}\mathrm{Ca}^{*},^{39}\mathrm{Ca}+\ensuremath{\gamma})X$. Such a dissipative reaction was recently characterized for the case of inelastic scattering of $^{38}\mathrm{Ca}$ off $^{9}\mathrm{Be}, ^{9}\mathrm{Be}(^{38}\mathrm{Ca}, ^{38}\mathrm{Ca}+\ensuremath{\gamma})X$. Additional data and discussion on the nuclear structure of $^{38}\mathrm{Ca}$ is also presented. An explanation for the more-complex-structure states, populated with small cross sections in one-nucleon knockout reactions, and observed in the tails of their longitudinal momentum distributions, is also offered.