We present scattering data from a melt of H-shaped polybutadiene polymers, in which the central crossbar of the polymers is wholly labeled with deuterium. The melt was uniaxially stretched by a factor of 2, and using careful temperature control of the sample, the neutron scattering pattern was measured after several different times of relaxation. The scattering data are compared against the predictions of a new theory, based upon the tube model but which includes the additional effect of elastic inhomogeneities in the entanglement network. We find that with this new theory one can obtain a good representation of the data, using parameters that are consistent with relaxation times obtained from a tube model description of the linear rheological data. The most important aspect of these data is an increasing anisotropy of the correlation hole peak, and this appears to be directly related to the elastic inhomogeneities. One further aspect of the comparison to theory is that the best fits are obtained using a Warner-Edwards tube diameter that deforms in a manner consistent with recent predictions for polymer networks.