  We develop an analytic model of intermittent, three-dimensional, strong,
reduced magnetohydrodynamic turbulence with zero cross helicity. We take the
fluctuation amplitudes to have a log-Poisson distribution and incorporate into
the model a new phenomenology of scale-dependent dynamic alignment. The
log-Poisson distribution in our model is characterized by two parameters. To
calculate these parameters, we make use of three assumptions: that the energy
cascade rate is independent of scale within the inertial range, that the most
intense coherent structures at scale $\lambda$ are sheet-like with a volume
filling factor proportional to $\lambda$, and that most of the cascade power
arises from interactions between exceptionally intense fluctuations and much
weaker fluctuations. We then compute the scalings of the power spectrum, the
kurtosis, higher-order structure functions, and three different average
alignment angles. These scalings appear to be consistent with numerous results
from direct numerical simulations.
