In this paper, we propose a new (single-step) block synchronisation algorithm for joint channel and DC-offset estimation for data-dependent superimposed training (DDST). While a (two-step) block synchronisation algorithm for DDST has previously been proposed in [5], due to interference from the information-bearing data it performed sub-optimally, resulting in channel estimates with unknown delays. These delay ambiguities (also present in the equaliser) were then estimated in [5] in a non-practical manner. In this paper we avoid the need for estimation of this delay ambiguity by exploiting the special structure of the channel output’s cyclic mean vector. The result is a BER performance superior to the DDST synchronisation algorithm first published in [5].