CurveCP is (was?) designed to be more lightweight and efficient than industry standards. 1-RTT session bootstrapping, forward secure encryption and authentication, per datagram public-key encryption, while leaving only the ephemeral public key, the connection ID, and per-message nonce in the clear.
While the ciphersuite employed in CurveCP (i.e., Curve25519) is being added to TLS (i.e., with draft-josefsson-tls-curve25519 and X25519 in Chrome), CurveCP is more amenable to be contrasted with DTLS and other transport security protocols working with datagrams, being based on UDP.