The P&P theory of UG has come under heavy criticism, lately, from outside but also from inside generative grammar. The claim is that the search for ‘deep parameters’ underlying clusters of properties across languages has led nowhere, and should be given up. I have revisited a theory, now two decades old, which explained ten syntactic differences between Insular and Mainland Scandinavian as the effects of a single parametric difference (in a series of works by C. Platzack and A. Holmberg). The theory is shown to be fundamentally right, descriptively and theoretically. Later developments in generative theory only serve to sharpen the formulations, adding another layer of explanatory depth to the earlier theory. The conclusion is that there are parameters of the traditional kind. The problems encountered when the theory is tested on more distantly related languages is discussed on the basis of facts from Finnish. P&P theory is perfectly consistent with the minimalist approach to UG and variation when parameters are seen as points of under-specification in UG, and restrictions on variation are seen as, in part, third factor effects, in the sense of Chomsky (Linguistic Inquiry 36: 1–22, 2005).