Syntactic methods of picture generation have become established during the last decade or two. We use random context picture grammars (rcpg s) to generate pictures. The productions of such a grammar are context-free, but their application is regulated---permitted or forbidden---by context randomly distributed in the developing picture. In previous work we investigated the most obvious subclasses of rcpgs, namely context free picture grammars (cfpgs), random permitting context picture grammars (rPcpgs) and random forbidding context picture grammars (rFcpgs) and developed characterisation theorems for them. We now introduce the notion of table-driven context-free picture grammars, and prove two characterisation lemmas for the corresponding picture sets. We show that these grammars are more powerful than context-free picture grammars, but strictly weaker than random forbidding context picture grammars. Moreover, we give results which show how these lemmas are limited in their application to galleries generated using permitting context only.