  We present the atmospheric structure and the fundamental parameters of three
red supergiants, increasing the sample of RSGs observed by near-infrared
spectro-interferometry. Additionally, we test possible mechanisms that may
explain the large observed atmospheric extensions of RSGs.
  We carried out spectro-interferometric observations of 3 RSGs in the
near-infrared K-band with the VLTI/AMBER instrument at medium spectral
resolution. To comprehend the extended atmospheres, we compared our
observational results to predictions by available hydrostatic PHOENIX,
available 3-D convection, and new 1-D self-excited pulsation models of RSGs.
  Our near-infrared flux spectra are well reproduced by the PHOENIX model
atmospheres. The continuum visibility values are consistent with a
limb-darkened disk as predicted by the PHOENIX models, allowing us to determine
the angular diameter and the fundamental parameters of our sources.
Nonetheless, in the case of V602 Car and HD 95686, the PHOENIX model
visibilities do not predict the large observed extensions of molecular layers,
most remarkably in the CO bands. Likewise, the 3-D convection models and the
1-D pulsation models with typical parameters of RSGs lead to compact
atmospheric structures as well, which are similar to the structure of the
hydrostatic PHOENIX models. They can also not explain the observed decreases in
the visibilities and thus the large atmospheric molecular extensions. The full
sample of our RSGs indicates increasing observed atmospheric extensions with
increasing luminosity and decreasing surface gravity, and no correlation with
effective temperature or variability amplitude, which supports a scenario of
radiative acceleration on Doppler-shifted molecular lines.
