We derive an effective Hamiltonian for a (001)-confined quasi-two-dimensional hole gas in a strained zinc-blende semiconductor heterostructure including both Rashba and Dresselhaus spin-orbit coupling. In the presence of uniaxial strain along the < 110 > axes, we find a conserved spin quantity in the vicinity of the Fermi contours in the lowest valence subband. In contrast to previous works, this quantity meets realistic requirements for the Luttinger parameters. For more restrictive conditions, we even find a conserved spin quantity for vanishing strain, restricted to the vicinity of the Fermi surface.