David Wishinsky over at Athletics Nation proposed the idea of a 'defensive independent perfect game," a concept which he proposed would simply be a standard Complete Game with no walks or homeruns allowed. Tom Tango over at the Book blog then expounded on the idea, lobbying that the feat also require no hit batsmen and a FIP of 0.00 (requiring K*2/ IP to be greater than 3.2).
In 9 innings of baseball that would require at least 15 strikeouts. Using the B-Ref play index, I found 12 performances that met this criteria:
FIP PERFECT GAMES