In this work we present a construction for symplectically reducing
quasi-morphisms on the universal cover $\widetilde{Ham}(M)$ of the Hamiltonian
group for certain symplectic K\"ahler manifolds, to quasi-morphisms on
$\widetilde{Ham}(\Si)$, where $\Si$ is a complex hypersurface of $M$. Along the
way we show that quasi-morphisms on $\widetilde{Ham}(M)$ that arise from
spectral invariants are the Calabi homomorphism when restricted to Hamiltonians
supported on stably displaceable sets.