On a strict cut you should probably avoid all bread products.. bagels especially.. wheat is better but not on a regular basis.
The only bagel-like product I've found that might be kinda good... Is Thomas's Bagel Square Bagel Bread in whole wheat... simple ingredient list, 50gs of carbs roughly, and an astonishing 9gs of fiber.
Again, problem is u get a bunch in a package, and u probably shouldnt be havint 1 a day all week.