High resolution γ-ray spectroscopy measurements at MHz counting rates were carried out at nuclear accelerators, combining a LaBr3(Ce) detector with dedicated hardware and software solutions based on digitization and post-mortem analysis. Spectra were reconstructed at counting rates up to 4 MHz, with little or no degradation of the energy resolution. The reported results represent a step forward towards the final goal of γ-ray spectroscopy measurements on a burning plasma device.