The objective of turbulence modeling is to capture the large scale structures in the flow without explicitly resolving the small scales structures that, over time, influence the large-scale structures. This is generally accomplished by adding regularization terms to the Navier-Stokes equations. We examine spectral viscosity models in which only the high-frequency spectral modes are regularized. The objective is to retain the large-scale dynamics while modeling turbulent fluctuationsa ccurately. We show that, unlike for the Navier-Stokes equations, there is no existence-uniqueness gap for the spectral viscosity models. Spectral regularization introduces a host of parameters to the model. We rigorously justify effective choices of parameters.