We have measured the vapor pressure above layers of solid hydrogen and deuterium, grown either directly onto a copper substrate or onto previously condensed argon layers, at temperatures in the range 1.6 to 5.2 K. A number of vapor pressure curves were obtained for each layer with different heat fluxes incident on the hydrogen layers. We could not achieve vapor pressures predicted by theory below 2.7 K. However, we conclude that there is no real vapor pressure anomaly but that due to the difference in phonon spectra between the hydrogen layer and the copper substrate there exists a difference in temperature between them even under extremely low heat loads. The results of our experiments are discussed in relation to the design of hydrogen cryopumps, gauge calibration and the conditions required for the condensation of H 2 on solid grains in interstellar gas clouds.