We discuss a new form of high-frequency hydrodynamics suitable for plasmon calculations in inhomogeneous systems. The theory naturally ensures the use of low- and high-frequency pressure coefficients in the appropriate limits: in particular it correctly brings in the low-frequency coefficient for rigid Kohn motion of parabolically confined systems. As an example we obtain both the Kohn mode and the correctly spaced standing plasmons of a parabolic quantum well. This is achieved starting from a smooth inhomogeneous self-consistent Thomas-Fermi groundstate density for the parabolic well. As a result neither arbitrary boundary conditions nor special system-specific assumptions are required for the hydrodynamic description.