I am presently experimenting with my Neon.
OEM Spec is 5w30 for 1995 to 2004, then in 2005 they switch to recommending 5w20. As best can be found, there was not an engine change to support this.
My last OCI I used M1 0w40 and my car did not respond well. However, with no recent data of my current usage, I don't know if it was the oil or engine that wasn't happy. I used 3.5 qts over 7000 miles. I originally went with the 0w40 to quiet down the valve train noise the Neons are known for, but what started quieter seemed to come back through the OCI.
Currently using PUP 5w20 and the verdict is still under deliberation as I don't have enough miles to see if there is a difference. Strange note is the engine seems quieter with this oil than the last.