There are two families of  influential and stubborn puzzles that face many theories of aboutness (intentionality), underdetermination puzzles and puzzles concerning representations that appear to be directed at things that do not exist. I propose an approach that elegantly avoids both kinds of puzzle. The central idea is to explain aboutness (the relation supposed to stand between thoughts and linguistic terms and their objects) in terms of relations of co-aboutness, also known as 'intentional identity' (the relation of being about the same thing that stands between the thoughts and linguistic terms themselves).