Oscillating-gradient spin echo (OGSE) diffusion experiments have long been used to measure the short-time apparent diffusion coefficient, D app ( t), in the presence of restricted diffusion, as well as the spectrum of the slow-motion velocity autocorrelation function. In this work, we focus on two previously unexplored aspects of OGSE experiments: convection compensation and acquisition of pure-phase diffusion spectra in the presence of homonuclear scalar couplings. We demonstrate that convection compensation afforded by single-echo OGSE compares well with that in double-echo convection-compensated PGSE experiments. We also show that, in the presence of homonuclear scalar couplings, setting the OGSE echo time to 1/2 J enables acquisition of pure-phase diffusion spectra and yields more reliable D estimates than mixed-phase PGSE or OGSE spectra. Pure-phase OGSE acquisition is also compatible with measurements of the apparent diffusion coefficient at an arbitrary diffusion time. These features of OGSE can be valuable in diffusion measurements of scalar-coupled small-molecule probes in cellular and other heterogeneous systems.