  Aims: We derive limits on the EBL density from the energy spectra of distant
sources of very high energetic gamma-rays (VHE gamma-rays). Methods: VHE
gamma-rays are attenuated by the photons of the EBL via pair production, which
leaves an imprint in the measured spectra from distant sources. In this paper
we present a new method to derive constraints on the EBL. Hereby, we use only
very basic assumptions about TeV blazar physics and no pre-defined EBL model,
but rather a large number of generic shapes constructed from a grid in EBL
density vs. wavelength. In our study we utilize spectral data from all known
TeV blazars, making this the most complete study so far. Results: We derive
limits on the EBL for three individual TeV blazar spectra (Mkn 501, H1426+428,
1ES1101-232) and for all spectra combined. Combining the results from
individual spectra leads to significantly stronger constraints over a wide
wavelength range from the optical (~ 1 micron) to the far-infrared (~ 80
microns). The limits are only a factor of 2 to 3 above the absolute lower
limits derived from source counts. In the mid-infrared our limits are the
strongest constraints derived from TeV blazar spectra so far. A high density of
the EBL around 1 micron, reported by direct detection experiments, can be
excluded. Conclusions: Our results can be interpreted in two ways: (i) The EBL
is almost resolved by source counts, leaving only little room for additional
components by e.g. the first stars or (ii) the assumptions about the underlying
physics are not valid, which would require substantial changes in the standard
emission models of TeV blazars.
