Individual estimates of cochlear compression may provide complementary information to traditional audiometric hearing thresholds in disentangling different types of peripheral cochlear damage. Here we investigated the use of the slope of envelope following response (EFR) magnitude-level functions obtained from four simultaneously presented amplitude modulated tones with modulation frequencies of 80-100 Hz as a proxy of peripheral level compression. Compression estimates in individual normal hearing (NH) listeners were consistent with previously reported group-averaged compression estimates based on psychoacoustical and distortion-product oto-acoustic emission (DPOAE) measures in human listeners. They were also similar to basilar membrane (BM) compression values measured invasively in non-human mammals. EFR-based compression estimates in hearing-impaired listeners were less compressive than those for the NH listeners, consistent with a reduction of BM compression. Cochlear compression was also estimated using DPOAEs in the same NH listeners. DPOAE estimates were larger (less compressive) than EFRs estimates, showing no correlation. Despite the numerical concordance between EFR-based compression estimates and group-averaged estimates from other methods, simulations using an auditory nerve (AN) model revealed that compression estimates based on EFRs might be highly influenced by contributions from off-characteristic frequency (CF) neural populations. This compromises the possibility to estimate on-CF (i.e., frequency-specific or "local") peripheral level compression with EFRs.