Transmission losses (TL) to highly impulsive signals generated by three firearms have been measured for two ear muffs, using both a head and torso simulator and a miniature microphone located at the ear canal entrance (MIRE technique). Peak SPL TL have been found to be well approximated by 40 ms short-L eq TL. This has allowed the use of transmissibilities and correction factors for bone conduction and physiological masking appropriate for continuous noise, for the calculation of REAT-type peak insertion losses (IL). Results indicate that peak IL can be well predicted by estimates based on one-third octave band 40 ms short L eq and manufacturer-declared (nominal) IL measured for continuous noise according to test standards. Such predictions tend to be more accurate at the high end of the range, while they are less reliable when the attenuation is lower. A user-friendly simplified prediction algorithm has also been developed, which only requires nominal IL and one-third octave sound exposure level spectra. Separate predictions are possible for IL in direct and diffuse sound fields, albeit with higher uncertainties, due to the smaller number of experimental data comprising the two separate datasets on which such predictions are based.