  One aspect of the quantum nature of spacetime is its "foaminess" at very
small scales. Many models for spacetime foam are defined by the accumulation
power $\alpha$, which parameterizes the rate at which Planck-scale spatial
uncertainties (and thephase shifts they produce) may accumulate over large
path-lengths. Here $\alpha$ is defined by theexpression for the path-length
fluctuations, $\delta \ell$, of a source at distance $\ell$, wherein $\delta
\ell \simeq \ell^{1 - \alpha} \ell_P^{\alpha}$, with $\ell_P$ being the Planck
length. We reassess previous proposals to use astronomical observations
ofdistant quasars and AGN to test models of spacetime foam. We show explicitly
how wavefront distortions on small scales cause the image intensity to decay to
the point where distant objects become undetectable when the path-length
fluctuations become comparable to the wavelength of the radiation. We use X-ray
observations from {\em Chandra} to set the constraint $\alpha \gtrsim 0.58$,
which rules out the random walk model (with $\alpha = 1/2$). Much firmer
constraints canbe set utilizing detections of quasars at GeV energies with {\em
Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $\alpha
\gtrsim 0.67$ and $\alpha \gtrsim 0.72$, respectively. These limits on $\alpha$
seem to rule out $\alpha = 2/3$, the model of some physical interest.
