For theories on lattice such as manifestly local chiral gauge theories, the longitudinal gauge degrees of freedom affect the dynamics of the physical sector in an undesirable manner. However, to control these redundant degrees of freedom, the standard Fadeev-Popov gauge-fixing procedure cannot be employed, since the Becchi-Rouet-Stora-Tyutin (BRST) symmetry of the off-shell Fadeev-Popov action with compact lattice gauge fields leads to an indeterminate 0/0 form for expectation value of any gauge-invariant operator. This work describes numerical investigation of proposals that evade the above no-go situation for both Abelian and non-Abelian lattice gauge theories.