We investigate transport properties of topologically disordered three-dimensional one-particle tight-binding models, featuring site-distance-dependent hopping terms. We start from entirely disordered systems into which we gradually introduce some short-range order by numerically performing a pertinent structural relaxation using local site-pair interactions. Transport properties of the resulting models within the delocalized regime are analyzed numerically using linear response theory. We find that even though the generated order is very short ranged, transport properties such as conductivity or mean free path scale significantly with the degree of order. Mean free paths may exceed the site-pair correlation length. It is furthermore demonstrated that while the totally disordered model is not in accord with a Drude- or Boltzmann-type description, moderate degrees of order suffice to render such a picture valid.