This work presents a novel protocol for fair exchange of DSA-based signatures to support an e-commerce activity of digital contract signing. The protocol employs an off-line semitrusted third party (STTP), which participates in the protocol execution only in exceptional circumstances and which involvement in the protocol is transparent. The protocol can tolerate the STTP's own misbehaviour (i.e. if it does not collude with other participants of the protocol) and it prevents the STTP from gaining the exchanged signatures or the signed document. The protocol is based on the principle of verifiable and recoverable signature encryption, and in comparison with related protocols is more efficient.