Masking By Moving (MByM), provides robust and accurate radar odometry measurements through an exhaustive correlative search across discretised pose candidates. However, this dense search creates a significant computational bottleneck which hinders real-time performance when high-end GPUs are not available. Utilising the translational invariance of the Fourier Transform, in our approach, f-MByM, we decouple the search for angle and translation. By maintaining end-to-end differentiability a neural network is used to mask scans and trained by supervising pose prediction directly. Training faster and with less memory, utilising a decoupled search allows f-MByM to achieve significant run-time performance improvements on a CPU (168%) and to run in real-time on embedded devices, in stark contrast to MByM. Throughout, our approach remains accurate and competitive with the best radar odometry variants available in the literature -- achieving an end-point drift of 2.01% in translation and 6.3deg/km on the Oxford Radar RobotCar Dataset.