  The binding energies of 29Si, 33S, and 36Cl have been measured with a
relative uncertainty $< 0.59 \times 10^{-6}$ using a flat-crystal spectrometer.
The unique features of these measurements are 1) nearly perfect crystals whose
lattice spacing is known in meters, 2) a highly precise angle scale that is
derived from first principles, and 3) a gamma-ray measurement facility that is
coupled to a high flux reactor with near-core source capability. The binding
energy is obtained by measuring all gamma-rays in a cascade scheme connecting
the capture and ground states. The measurements require the extension of
precision flat-crystal diffraction techniques to the 5 to 6 MeV energy region,
a significant precision measurement challenge. The binding energies determined
from these gamma-ray measurements are consistent with recent highly accurate
atomic mass measurements within a relative uncertainty of $4.3 \times 10^{-7}$.
The gamma-ray measurement uncertainties are the dominant contributors to the
uncertainty of this consistency test. The measured gamma-ray energies are in
agreement with earlier precision gamma-ray measurements.
