With the goal to thwart known attacks on the conceptual public key encryption scheme Polly Cracker, Ly constructed the Polly Two encryption scheme. The set-up of this new asymmetric encryption scheme is more sophisticated than that of Polly Cracker, and the new proposal seems to fix several known problems. The talk considers a heuristic attack on Polly Two, that aims at recovering the plaintext from a given ciphertext without revealing the secret key. The discussed approach in particular allows to solve the most recent "Polly Two challenge".