  We present a theory of spontaneous Fermi surface deformations for half-filled
Landau levels (filling factors of the form $\nu=2n+1/2$). We assume the
half-filled level to be in a compressible, Fermi liquid state with a circular
Fermi surface. The Landau level projection is incorporated via a modified
effective electron-electron interaction and the resulting band structure is
described within the Hartree-Fock approximation. We regulate the infrared
divergences in the theory and probe the intrinsic tendency of the Fermi surface
to deform through Pomeranchuk instabilities. We find that the corresponding
susceptibility never diverges, though the system is asymptotically unstable in
the $n \to \infty$ limit.
