I consider models with an impurity spin coupled to a fluctuating Gaussian field with or without additional Kondo coupling of the conventional sort. In the case of isotropic fluctuations, the renormalization-group flows for these models have controlled fixed points when the autocorrelation of the Gaussian field $h(t),$ $〈\mathrm{Th}(t)h(0)〉\ensuremath{\sim}{1/t}^{2\ensuremath{-}\ensuremath{\epsilon}}$ with small positive $\ensuremath{\epsilon}.$ In the absence of any additional Kondo coupling, I get power-law decay of spin correlators, $〈\mathrm{TS}(t)S(0)〉\ensuremath{\sim}{1/t}^{\ensuremath{\epsilon}}.$ For negative $\ensuremath{\epsilon},$ the spin autocorrelation is constant in long-time limit. The results agree with calculations in Schwinger Boson mean-field theory. In presence of a Kondo coupling to itinerant electrons, the model shows a phase transition from a Kondo phase to a field fluctuation dominated phase. These models are good starting points for understanding behavior of impurities in a system near a zero-temperature magnetic transition. They are also useful for understanding the dynamical local mean-field theory of Kondo lattice with Heisenberg (spin-glass-type) magnetic interactions as well as for understanding spin-fluid solutions near Mott transition in $t\ensuremath{-}J$ model.