  Bragg diffraction has been used in atom interferometers because it allows
signal enhancement through multiphoton momentum transfer and suppression of
systematics by not changing the internal state of atoms. Its multi-port nature,
however, can lead to parasitic interferometers, allows for intensity-dependent
phase shifts in the primary interferometers, and distorts the ellipses used for
phase extraction. We study and suppress these unwanted effects. Specifically,
phase extraction by ellipse fitting and the resulting systematic phase shifts
are calculated by Monte Carlo simulations. Phase shifts arising from the
thermal motion of the atoms are controlled by spatial selection of atoms and an
appropriate choice of Bragg intensity. In these simulations, we found that
Gaussian Bragg pulse shapes yield the smallest systematic shifts. Parasitic
interferometers are suppressed by a "magic" Bragg pulse duration. The
sensitivity of the apparatus was improved by the addition of AC Stark shift
compensation, which permits direct experimental study of sub-part-per-billion
(ppb) systematics. This upgrade allows for a 310\,$\hbar k$ momentum transfer,
giving an unprecedented 6.6\,Mrad measured in a Ramsey-Bord\'e interferometer.
