  We present results from three-dimensional hydrodynamic simulations of the
high redshift collapse of pregalactic clouds including feedback effects from a
soft H2 photodissociating UV radiation field. The simulations use an Eulerian
adaptive mesh refinement technique to follow the nonequilibrium chemistry of
nine chemical species with cosmological initial conditions drawn from a popular
Lambda-dominated cold dark matter model. The results confirm that the soft UV
background can delay the cooling and collapse of small halos (~10^6 Msun). For
reasonable values of the photo-dissociating flux, the H2 fraction is in
equilibrium throughout most of the objects we simulate. We determine the mass
threshold for collapse for a range of soft-UV fluxes and also derive a simple
analytic expression. Continuing the simulations beyond the point of initial
collapse demonstrates that the fraction of gas which can cool depends mostly on
the virial mass of the halo and the amount of soft-UV flux, with remarkably
little scatter. We parameterize this relation, for use in semi-analytic models.
