Third-Best Economists?

Dani Rodrik, Havard economist and blogger, recently lamented that many economists discount the potential for market failure, especially in international trade calling them "First-Best Economists", because they believe we live in a first-best world. He contrasts this with his own views, that acknowledge that we live in a second-best world and that goverments have a role in correcting these market failures. Does that make economists who believe that market failures are real but that government failures are just as real and probably more pernicious and problematic are Third-Best Economists?

Adendum: Tyler Cowen suggests that he is in fact a fourth or a fifth best economist...