The bisector of two rational surfaces in R/sup 3/ is, in general, nonrational; and so is the bisector of a rational curve and a rational surface. Thus, bisector surfaces in these two cases must be approximated numerically. Unfortunately, they are algebraic surfaces of very high degree and numerical approximation is non-trivial. This paper suggests a new computational model for constructing curve-surface and surface-surface bisectors in R/sup 3/. The curve-surface bisector problem is reformulated as the search for a trivariate zero-set; and the surface-surface bisector problem is reduced to that of finding the common zero-set of two four-variate functions.