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; wherein the first and second vertex shading operations are performed by executing respective vertex shading programs for those operations, and the method further comprises: generating the vertex shading programs for the first and second vertex shading operations by modifying the vertex shading program supplied by the application that requires the graphics processing in question by: for the vertex shading program for the first vertex shading operation, removing one or more output attributes from the vertex shading program supplied by the application and recompiling the vertex shading program; and for the vertex shading program for the second vertex shading operation, removing from the vertex shading program supplied by the application one or more output attributes that will be processed by the first vertex shading program and recompiling the vertex shading program.