A partial wall-flow filter having some unplugged flow-through channels and some plugged channels. Desirable combinations of filtration efficiency and back pressure may be provided by combinations of t wall≦305 urn, MPD≦20 μm, % P≧50%, and CD≧250 cpsi wherein t wall is the transverse thickness of the porous walls, MPD is a mean pore diameter of the porous walls, % P is the total porosity of the porous walls, and CD is the cell density of the channels. In one embodiment, some of the plugged channels are located adjacent to the inlet end and some are located adjacent to the outlet end. Systems and method including the partial wall-flow filter are also described.