An experimental study was carried out to examine the rheological behavior of polymer melts in laminar flows through channels with small-angle convergences (2-3 degrees) and spiralling walls (6 degrees /mm along the flow direction), using an extrusion grade of low-density polyethylene. The results show that convergence is the main factor responsible for the observed deviations from steady state laminar shear flow, particularly with respect to additional pressure requirements to maintain a constant mass output. The swell ratio, calculated from the dimensions of the channel at the exit, was found to be considerably higher for flow-through converging channels. Only a small increase in swell ratio could be attributed, on the other hand, to the rotational elements of the die configuration. It is inferred that even for small angles of convergence the increased level of swelling is associated with elongational stress components, which were grouped together and denoted as the "additional stress." This was obtained from the difference between the calculated average shear stress at the wall, using the recorded pressure at the die entry, and the value of the average shear stress at the wall calculated from the shear viscosity data for the melt.