We present a complete description of 2-dimensional equations that arise as symmetry reductions of four 3- dimensional Lax-integrable equations: (1) the universal hierarchy equation $u_{yy} = u_zu_{xy}− u_yu_{xz}$; (2) the 3D rdDym equation $u_{ty} = u_xu_{xy}− u_yu_{xx}$; (3) the equation $u_{ty} = u_tu_{xy}− u_yu_{tx}$, which we call modified Veronese web equation; (4) Pavlov's equation $u_{yy} = u_{tx} + u_yu_{xx}− u_xu_{xy}$.