Less than half an inch should be ok! The largest often recommended for a green cheek conure sized bird is 5/8's, which equals 10/16, and 11/16th isn't much bigger. One might even be able to get away with 3/4's inch spacing (or 12/16) but you could be pushing it, depending on the size of the green cheek. Green cheeks can range in size from 50 some grams on up to 80 some grams, so a smaller green cheek may not do well in a cage that has 3/4" bar spacing.