  The quantization scheme based on reduction of the physical states
\cite{Park:2014tia} is extended to two gravity-matter systems and pure dS
gravity. For the gravity-matter systems we focus on quantization in a flat
background for simplicity, and renormalizability is established through
gauge-fixing of matter degrees of freedom. Quantization of pure dS gravity has
several new novel features. It is noted that the infrared divergence does not
arise in the present scheme of quantization. The lapse function constraint
plays a crucial role.
