  Contributions of $D$ waves to physical observables for neutral pion
photoproduction from the proton in the near-threshold region are studied and
means to isolate them are proposed. Various approaches to describe the
multipoles are employed
  --a phenomenological one, a unitary one, and heavy baryon chiral perturbation
theory. The results of these approaches are compared and found to yield
essentially the same answers. $D$ waves are seen to enter together with $S$
waves in a way that any means which attempt to obtain the $E_{0+}$ multipole
accurately must rely on knowledge of $D$ waves and that consequently the latter
cannot be dismissed in analyses of low-energy pion photoproduction. It is shown
that $D$ waves have a significant impact on double-polarization observables
that can be measured. This importance of $D$ waves is due to the soft nature of
the $S$ wave and is a direct consequence of chiral symmetry and the
Nambu--Goldstone nature of the pion. $F$-wave contributions are shown to be
negligible in the near-threshold region.
