This paper is a detailed critical study of Adolf Grünbaum's work on the Duhemian thesis. I show that (a) Grünbaum's geometrical counterexample to the (D1) subthesis is unsuccessful, even with minimal claims made for what the counterexample is supposed to show, and (b) the (D2) subthesis is not a reasonable one (and cannot correctly be attributed to Duhem). The paper concludes with an argument about the relation between the Duhemian thesis, concerning component hypotheses of a scientific theory, and the view that it is impossible to falsify entire theories conclusively.