1. A method of operating a graphics processing pipeline that includes vertex shading circuitry that performs vertex shading operations on vertex attribute data to generate vertex-shaded vertex attribute data, the method comprising: for a set of vertices to be processed by the graphic processing pipeline: (i) performing a first vertex shading operation on one or more vertices of the set of vertices, wherein the first vertex shading operation comprises performing, for the one or more vertices of the set, vertex shading processing for at least one but not all of the vertex attributes of the vertex or vertices in question, to generate vertex shaded attribute data for those attributes of the vertex or vertices; (ii) determining, for a vertex or vertices that have been subjected to the first vertex shading operation, whether the vertex or vertices in question should be processed further, using, at least in part, some or all of the vertex shaded attribute data generated by the first vertex shading operation; and (iii) performing a second vertex shading operation on a vertex or vertices that it has been determined should be processed further, wherein the second vertex shading operation comprises performing vertex shading processing for at least one other vertex attribute of the plurality of vertex attributes belonging to the vertex in question, to generate vertex shaded attribute data for the at least one other attribute of the vertex or vertices.