An important characteristic of a polymer is its molecular weight distribution (MWD). The MWD affects its processing characteristics and its solid state performance. The traditional analytical method for determining MWD is gel permeation chromatography (GPC). However, GPC results depend strongly on the skill and experience of the operator and are not sensitive to small amounts of high molecular weight material that can have an important effect on processing and product properties. It is known that rheological properties depend on MWD, and it has been proposed that viscosity or complex viscosity data can be used to infer the MWD for commercial polymers. Although there has been some controversy as to whether this is feasible, recent results of Shaw, Tuminello, and others indicate that for linear polymers this is, in theory, possible. However, limitations in the accessible frequency range, as well as inevitable experimental errors, pose serious barriers to the use of such a procedure. We have investigated the severity of these barriers and have shown that within certain limits, complex viscosity data can be used to infer a realistic MWD for linear polyethylenes.