We investigate how whole populations of 2–6 MeV electrons can be quickly lost from the Earth's outer radiation belt at L= 3–6 through precipitation into the atmosphere due to quasi‐linear pitch angle scattering by combined electromagnetic ion cyclotron (EMIC) and whistler mode waves of realistic intensities occurring at the same or different local times. We provide analytical estimates of the corresponding relativistic electron lifetimes, emphasizing that the combined effects of both waves can lead to very fast (2–10 h) dropouts. Scaling laws for the loss timescales are derived, allowing us to determine the various plasma and wave parameter domains potentially leading to strong and fast dropouts. The analysis reveals that the fastest MeV electron dropouts occur at approximately the same rate over some high energy range and almost independently of EMIC wave amplitudes above a certain threshold. These results should help to better understand the dynamic variability of the radiation belts. Key Points Combined EMIC and chorus or hiss scattering can cause fast and strong MeV electron dropouts Comprehensive parametric study of this dropout mechanism based on analytical estimates Dropout timescales become independent of electron energy and EMIC intensity for sufficiently high EMIC to chorus wave intensity ratio