In VeryLEED regime (below 30 eV) the spectra of electron reflection on
the surfaces of crystals are dominated by the elastic effects of bulk
E(k) above the vacuum level. This is revealed when the reflected inte
nsity is found by matching on the surface the wavefunction in vacuum (
plane waves) and in the solid (Bloch waves). Following reflectivity fe
atures versus energy and incidence angle, one can extract accurate and
explicit information on upper E(k): the energies of extremes of bands
along any Brillouin zone direction, and even whole bands along symmet
ry lines. This is illustrated with a profusion of experimental example
s. The theoretical background and the experimental technique are surve
yed. Capabilities of VeryLEED to generate the upper bands for PES (IPE
S) are outlined.