An overview of seismic, thermal, and petrological evidence on the structure of Precambrian lithosphere suggests that its local maximum thickness is highly variable (140-350 km), with a bimodal distribution for Archean cratons (200-220 km and 300-350 km). We discuss the origin of such large differences in lithospheric thickness, and propose that the lithospheric base can have large depth variations over short distances. The topography of Bryce Canyon (western USA) is proposed as an inverted analog of the base of the lithosphere. The horizontal and vertical dimensions of Archean cratons are strongly correlated: larger cratons have thicker lithosphere. Analysis of the bimodal distribution of lithospheric thickness in Archean cratons shows that the "critical" surface area for cratons to have thick (>300 km) keels is >6-8 ?? 106 km2 . Extrapolation of the linear trend between Archean lithospheric thickness and cratonic area to zero area yields a thickness of 180 km. This implies that the reworking of Archean crust should be accompanied by thinning and reworking of the entire lithospheric column to a thickness of 180 km in accord with thickness estimates for Proterozoic lithosphere. Likewise, extrapolation of the same trend to the size equal to the total area of all Archean cratons implies that the lithospheric thickness of a hypothesized early Archean supercontinent could have been 350-450 km decreasing to 280-400 km for Gondwanaland. We evaluate the basal drag model as a possible mechanism that may thin the cratonic lithosphere. Inverse correlations are found between lithospheric thickness and (a) fractional subduction length and (b) the effective ridge length. In agreement with theoretical predictions, lithospheric thickness of Archean keels is proportional to the square root of the ratio of the craton length (along the direction of plate motion) to the plate velocity. Large cratons with thick keels and low plate velocities are less eroded by basal drag than small fast-moving cratons. Basal drag may have varied in magnitude over the past 4 Ga. Higher mantle temperatures in the Archean would have resulted in lower mantle viscosity. This in turn would have reduced basal drag and basal erosion, and promoted the preservation of thick (>300 km) Archean keels, even if plate velocities were high during the Archean.