Partially premixed cool flames have been modeled numerically and then experimentally established in an ozone-assisted counterflow burner using dimethyl ether as a fuel. A double flame structure, consisting of a cool diffusion flame and a cool premixed flame, has been found computationally at moderate strain rates. The impact of ozone on the low-temperature chemistry and radical pool can be seen in the structure of the premixed flame, where the fuel is more fully oxidized and the heat release is greater than the diffusion flame. It is also found that high-temperature ignition is more sensitive to fuel addition in the premixture due to enhanced production of HO2. Experimental results support the existence of the double cool flame structure and the increased reactivity of the premixed cool flame.