This paper introduces CCFB and CCFB+H, two patent-free authenticated encryption schemes. CCFB+H also supports the authentication of associated data. Our schemes can employ any block cipher and are provably secure under standard assumptions. The schemes and their proofs of security are simple and straightforward. CCFB and CCFB+H restrict the sizes of nonce and authentication tags and can, depending on these sizes, perform significantly better than both generic composition and other two-pass schemes for authenticated encryption, such as the EAX mode.