  We present theoretical and dynamic Monte Carlo simulation results for the
mobility and microscopic structure of 1+1-dimensional Ising interfaces moving
far from equilibrium in an applied field under a single-spin-flip ``soft''
stochastic dynamic. The soft dynamic is characterized by the property that the
effects of changes in field energy and interaction energy factorize in the
transition rate, in contrast to the nonfactorizing nature of the traditional
Glauber and Metropolis rates (``hard'' dynamics). This work extends our
previous studies of the Ising model with a hard dynamic and the unrestricted
SOS model with soft and hard dynamics. [P.A. Rikvold and M. Kolesik, J. Stat.
Phys. 100, 377 (2000); J. Phys. A 35, L117 (2002); Phys. Rev. E 66, 066116
(2002).] The Ising model with soft dynamics is found to have closely similar
properties to the SOS model with the same dynamic. In particular, the local
interface width does not diverge with increasing field, as it does for hard
dynamics. The skewness of the interface at nonzero field is very weak and has
the opposite sign of that obtained with hard dynamics.
