Necessary ingredients of {\em accurate} empirical Galerkin models for incompressible free and wall-bounded shear flows are discussed. These models are based on the Karhunen-Lo\`eve (K-L) decomposition of a Navier-Stokes simulation and a Galerkin projection on the Navier-Stokes equation. Specifically, a novel analytical pressure-term representation is first developed and shown to be necessary for accurate Galerkin systems of near-field wakes and of mixing layers. Secondly, a hierarchy of `subgrid' turbulence models based on Rempfer's (1991) modal eddy viscosities is presented and shown to be helpful if a low-dimensional K-L ansatz does not resolve a significant portion of the fluctuation energy. Finally, the role of `missing' phase space directions in the K-L ansatz is revisited and additional modes are proposed. The proposed generalizations and improvements have been integrated in a modular Galerkin `tool-box' with a hierarchy of procedures to determine model coefficients.