The Wolff cluster Monte Carlo algorithm accelerates lattice stat-mech
models near criticality. External fields, ignored by Wolff, are of
significant current importance, e.g. for information geometry, universal
scaling of correlation functions, and essential singularities in critical
properties just in our group. We evaluate a little-known extension to 
Wolff (e.g., unknown to expert Jon Machta) to demonstrate that it 
largely eliminates critical slowing down in a variety of models, and 
generalize the extension to arbitrary fields.