We investigate new realisations of the W3 algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with c = 102 and c = 100 to build non-critical and critical W3 BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string with c = 28 f- 2, together with a Kugo-Ojima topological term. Consequently, these realisations provide embeddings of the Virasoro string into non-critical and critical W3 strings.