The irregular nature of vertical profiles of density in the thermocline appears well described by a Poisson process over vertical scales 2-200 m. To what extent does this view of the thermocline conflict with established models of the internal wavefield? Can a one-parameter Poisson subrange be inserted between the larger-scale wavefield and the microscale field of intermittent turbulent dissipation, both of which require many parameters for their specification? It is seen that a small modification to the Poisson vertical correlation function converts it to the corresponding correlation function of the Garrett Munk internal wave spectral model. The linear scaling relations and vertical wavenumber dependencies of the GM model are maintained provided the Poisson constant κ0 is equated with the ratio of twice the displacement variance to the vertical correlation scale of the wavefield. Awareness of this Poisson Wavefield Relation enables higher order strain statistics to be determined directly from the strain spectrum. Using observations from across the Pacific Ocean, the average Thorpe Scale of individual overturning events is found to be nearly equal to the inverse of the κ0 that characterizes the background thermocline in which the events occur. If the “fractional occurrence of overturning”, ϕ, is introduced as an additional parameter, a Poisson version of the Gregg-Henyey relationship can be derived. The Poisson constant, buoyancy frequency, and ϕ combine to create a complete parameterization of energy transfer from internal wave scales through the Poisson subrange to dissipation. An awareness of the underlying Poisson structure of the thermocline will hopefully facilitate further improvement in both internal wave spectral models and ocean mixing parameterizations.