Numerical models demonstrate that a boundary layer instability of the lower lithosphere does not stop the lithosphere from subsiding, and so it cannot explain the so-called flattening of old seafloor. The slower subsidence of the old seafloor is in any case better seen as a perturbation, probably due to plumes. Furthermore, if a boundary layer instability, or any mode of upper mantle convection, transported most of the heat emerging from old seafloor, there would be pervasive, large-amplitude local bathymetric, gravity, and geoid anomalies. Such anomalies have never been convincingly differentiated from the effects of the cooling lithosphere and hotspot tracks, expect for some low-amplitude, linear geoid anomalies near spreading centers. The only modes of mantle convection with horizontal scales less than those of plates for which there is reasonably clear evidence are hotspot plumes and some possible near-ridge boundary layer instabilities. Hotspots transport less than about 10% of the Earths heat flux, and other small-scale modes are probably less important.