Abstract
Helium films are explored in the temperature range 1-2.8 K for thicknesses of 3-11 atomic layers. Sharp heat-capacity peaks for the thinnest films appear to indicate melting of the second-layer solid. Thicker films display coverage-dependent truncations of the λ-point specific-heat anomaly, and cell thermal conductivity shows abrupt changes near these truncation points. Comparison with mass-flow measurements leads to the discussion of a possible intermediate superfluid phase.