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We present the results of a visible spectroscopic survey of igneous asteroids belonging to the small and intriguing E-class, including 2867 Steins, a target of the Rosetta mission. The survey was carried out at the 3.5 m Telescopio Nazionale Galileo (TNG), and at the 3.5 m New Technology Telescope (NTT) of the European Southern Observatory. We obtained new visible spectra for eighteen E-type asteroids, and near infrared spectra for eight of them. We confirm the presence of three different mineralogies in the small E-type populations. We classify each object in the E[I], E[II] or E[III] subgroups [Gaffey, M.J., Kelley, M.S., 2004. Lunar Planet. Sci. XXXV. Abstract 1812] on the basis of the spectral behavior and of the eventual presence of absorption features attributed to sulfides (such the 0.49 μm band, on E[II]), or to iron bearing silicates (0.9 μm band, on E[III]). We suggest that some asteroids (i.e. 64 Angelina, 317 Roxane, and 434 Hungaria), which show different spectral behavior comparing our data with those available in literature, have an inhomogeneous surface composition. 2867 Steins, a target of the Rosetta mission, shows a spectral behavior typical of the E[II] subgroup, as already suggested by Barucci et al. [Barucci, M.A., Fulchignoni, M., Fornasier, S., Dotto, E., Vernazza, P., Birlan, M., Binzel, R.P., Carvano, J., Merlin, F., Barbieri, C., Belskaya, I., 2005. Astron. Astrophys. 430, 313–317] and Fornasier et al. [Fornasier, S., Marzari, F., Dotto, E., Barucci, M.A., Migliorini, A., 2007. Astron. Astrophys. 474, 29–32]. Litva and 1990 TN1, initially classified as E-types, show a visible and near infrared behavior consistent with the olivine rich A-class asteroids, while 5806 Archieroy, also supposed to belong to the E-class, has a spectral behavior consistent with the S(V) classification following the Gaffey et al. [Gaffey, M.J., Burbine, T.H., Piatek, J.L., Reed, K.L., Chaky, D.A., Bell, J.F., Brown, R.H., 1993. Icarus 106, 573–602] classification scheme. To fully investigate the E-type population, we enlarged our sample including 6 E-type asteroids spectra available in literature, resulting in a total sample of 21 objects. The analysis of the spectral slope for the 3 different E-type subgroups versus the orbital elements show that E[III] members have the lowest mean spectral slope value inside the whole sample, and that they are located between 2.2–2.7 AU in low inclination orbits. E[II] members has the highest spectral slope inside the sample, half of them are located in the Hungaria region, 2 are NEA and 2 (64 Angelina and 2867 Steins), are in the main belt. A similar distribution is found for the 5 featureless E[I] members, located mainly in the Hungaria region (3 members), one in the middle main belt while one is a NEA (2004 VD17). Finally, for the five E-type asteroids observed both in the visible and near infrared range, plus 2867 Steins, we attempt to model their surface composition using linear geographical mixtures of no more than 3 components, selected from aubrite meteorites and correlated minerals. In particular we suggest that the aubrite Peña Blanca might have the E[III] Asteroid 317 Roxane as parent body, and that the aubrite ALH78113 might be related to the E[II] subgroup asteroids.