We study the dynamical evolution of globular clusters containing populations
of primordial binaries, using our newly updated Monte Carlo cluster evolution
code with the inclusion of direct integration of binary scattering interactions.
We describe the modifications we have made to the code, as well as improvements
we have made to the core Monte Carlo method. We present several test calculations
to verify the validity of the new code, and perform many comparisons with previous
analytical and numerical work in the literature. We simulate the evolution of a large
grid of models, with a wide range of initial cluster profiles, and with binary
fractions ranging from 0 to 1, and compare with observations of Galactic
globular clusters. We find that our code yields excellent agreement with
direct N-body simulations of clusters with primordial binaries, but yields some
results that differ significantly from other approximate methods. Our
results for the structural parameters of clusters during the binary-burning
phase are outside the range of parameters for observed clusters, implying that
either clusters are born significantly more or less centrally concentrated than
has been previously considered, or that there are additional physical processes
beyond two-body relaxation and binary interactions that affect the structural characteristics
of clusters.