Detached eddy simulation is used to simulate the flow field around gaseous jets injected into supersonic crossflows. The simulations are done with and without the use of synthetic inflow generation, a method used to provide a realistic, time-varying boundary layer for the inflow condition of the simulations. The goal is to assess the ability of DES to simulate the complicated flow field around the injection location, and to assess the ability of synthetic inflow generation to capture the contribution of the preinjection boundary layer to the flow field. Reynolds stresses and turbulent kinetic energy predicted by the simulations are compared to experimentally measured values in one test case of normal injection of air into a Mach 1.6 freestream. A second test case compares predicted mean injectant mole fractions with measured values for a pair of staged injectors that inject air into a Mach 2 freestream. Unlike previous simulations of jets in supersonic crossflows done by the authors, the DES provides highly unsteady jet plumes, even without the synthetic inflow boundary layer. This is due partially to improved mesh resolution, but is mostly due to large and highly energetic separation regions upstream of the normal injectors, compared to smaller, less energetic regions upstream of the angled injectors simulated previously. As a result of the natural instability of these configurations, the role of the boundary layer structures is found to be small. However, the results show that DES reproduces the mean and fluctuating quantities very well compared to the measured values.