The effect of varying the solids volume fraction of an aqueous clay paste suspension on its printability via an Additive Manufacturing (AM) or 3D printing technique, Direct Ink Writing (DIW) or material extrusion, has been studied. DIW is a cost-effective and straightforward fabrication technology suitable for adoption at a larger scale by the traditional ceramics industry and the creative community. The pastes were prepared with volume fraction of solids ranging from 25–57 vol%. Their rheological properties (storage modulus and apparent yield stress) were measured by dynamic oscillatory rheometry. The relationships between solids content, rheological behaviour and print parameters were evaluated. An equation based on rheological properties to delineate between printable and non-printable conditions has been proposed. Several decorative pieces have been produced for architectural purposes.