Very-high energy observations of blazars can be used to constrain the strength of the intergalactic magnetic field .
A simplifying assumption which is often made is that of a magnetic field of constant strength composed by randomly oriented and identical cells .
In this paper , we demonstrate that a more realistic description of the structure of the intergalactic magnetic field is indeed needed .
If such a description is adopted , the observational bounds on the field strength are significantly affected in the limit of short field correlation lengths : in particular , they acquire a dependence on the magnetic field power spectrum .
In the case of intergalactic magnetic fields which are generated causally , for which the magnetic field large scale spectral index is n _ { B } \geq 2 and even , the observational lower bound becomes more constraining by about a factor 3 .
If instead -3 < n _ { B } < -2 , the lower bound is significantly relaxed .
Such magnetic fields with very red spectra can in principle be produced during inflation , but remain up to now speculative .