A linear θ-pinch discharge without preionization is investigated in Helium within that range of density, in which the mean free path of electrons between two elastic collisions diminishes to such a low value that the electrons cannot gain the ionization energy in the induced electric field over this distance. Compared to the well known observations at low densities in this high density range the instant of the first breakdown in the discharge tube is found to be shifted to later halfcycles with increasing initial pressure. In addition, the further development of the discharge at high initial densities shows a very different structure compared to the low density behaviour. Comparison of optical observations with measurements of the current density distribution obtained by means of magnetic probes (using a special difference method on account of the very small plasma currrents) shows the following result: In the half cycle immediately following the breakdown, a typical shock wave pinch is produced at high densities. The regions near the axis are heated only by an ionizing shock, while the contraction of the current sheath, which initially started the shock, is stopped very early in far outer regions. During the following half-cycle quite a different behaviour of the discharge is observed on account of the enhanced electrical conductivity: The contraction runs much faster and therefore the separation between the shock front and the driving current sheath decreases.