Studies of postglacial rebound (PGR) constrain the viscosity of the mantle in an absolute sense, and have also been used to constrain the radial variation in mantle viscosity. Such radial variations probably have important effects on many aspects of solid-earth dynamics, including the existence and style of plate tectonics, rotational dynamics, thermal convection, and mixing of chemical species by convection. Most studies of PGR, as well as other studies constraining viscosity structure (e.g. the geoid), agree that the average viscosity of the upper mantle (beneath the lithosphere) is smaller than that of the lower mantle. However, there is marked disagreement regarding the amount of viscosity contrast and the thickness of an upper mantle ‘low viscosity zone’ (LVZ), with estimates for the viscosity contrast ranging from a mere factor of 2 to several orders of magnitude. Here we seek to both quantify and clearly illustrate the fundamental modelling trade-off between viscosity contrast (η*) and layer thickness (D), and show that if only long-wavelength constraints are available, PGR models are largely indistinguishable for constant values of η*/D3 characterizing an LVZ. Models employing both relative sea level (RSL) data from Hudson Bay and time-variations in gravity from the GRACE satellite illustrate this principle. Models with LVZ viscosity contrasts ranging from <1 to >3 orders of magnitude fit the data equally well, depending on the thickness of the LVZ. Other traditional data sets constraining PGR (e.g. Fennoscandian strand lines) appear no more capable of independently resolving this ambiguity, although some studies that incorporate both long-wavelength (RSL) type constraints and shorter wavelength constraints, such as tilting of continental margins, appear to favour a relatively thin, high viscosity contrast LVZ. New GPS data from North America and Scandinavia may be able to resolve this question even further. However, at the present time PGR studies do not preclude, and perhaps favour, a relatively thin LVZ of viscosity contrast at least one and perhaps as much as 3 orders of magnitude beneath the lithosphere in some regions. This conclusion has significant implications for understanding the phenomenon of plate tectonics and the evolution and dynamics of the mantle.