A method of operating a gasifier is provided that envisions dividing the gasifier into multiple zones. A high-calorific-value feedstock with an oxidant is injected in the first zone. The gasifier is operated to substantially consume the oxidant within the first gasification zone. The method of operating the gasifier further includes injecting a low-calorific-value, high-oxygen-content feedstock in a second gasification zone. The low-calorific-value, high-oxygen-content feedstock is devolatilized and gasified in second zone. A method of operation provides for a synergistic co-gasification of the high-calorific-value feedstock and the low-calorific-value, high oxidant content feedstock. The method provides for specific control actions that enable operation of multi-fuel, multizone gasifier.