In this paper we first analyse the possibility for deniability under a strong adversary, who has an Internet-wide transcript of the communication. Secondly, we present a scheme which provides the desirable properties of previous messaging schemes, but with stronger deniability under the new adversary model. Our scheme requires physical meetings for exchanges of large amounts of random key-material via near-field communication and later uses this random data to key a one-time pad for text-messaging. We prove the correctness of the protocol and, finally, we evaluate the practical feasibility of the suggested scheme.