  We constrain blastwave parameters and the circumburst media of a subsample of
ten BeppoSAX Gamma-Ray Bursts. For this sample we derive the values of the
injected electron energy distribution index, p, and the density structure index
of the circumburst medium, k, from simultaneous spectral fits to their X-ray,
optical and nIR afterglow data. The spectral fits have been done in count space
and include the effects of metallicity, and are compared with the previously
reported optical and X-ray temporal behaviour. Using the blastwave model and
some assumptions which include on-axis viewing and standard jet structure,
constant blastwave energy and no evolution of the microphysical parameters, we
find a mean value of p for the sample as a whole of 2.04 +0.02/-0.03. A
statistical analysis of the distribution demonstrates that the p values in this
sample are inconsistent with a single universal value for p at the 3-sigma
level or greater, which has significant implications for particle acceleration
models. This approach provides us with a measured distribution of circumburst
density structures rather than considering only the cases of k=0 (homogeneous)
and k=2 (wind-like). We find five GRBs for which k can be well constrained, and
in four of these cases the circumburst medium is clearly wind-like. The fifth
source has a value of 0<k<1, consistent with a homogeneous circumburst medium.
