Compact binaries consisting of black holes, neutron stars, gravastars or boson stars undergo a post-Newtonian evolution sensitive to both the spins and mass quadrupole moment of the components. It is known that for particular spin configurations or values of the quadrupole parameter the so-called spin flip-flop effect occurs. This covers the wobbling of the spin successively from the North to South Pole and backwards on a timescale of several precessional periods but shorter than the gravitational-radiation timescale. The project aims to derive the gravitational waveform in this parameter range and identify the traces of the spin flip-flop effect imprinted into the low-frequency gravitational wave to be detected by the Laser Interferometer Space Antenna (LISA), recently approved by European Space Agency.