In “The Two Towers”, Chapter 2, “The Riders of Rohan”, Eomer is talking about Saruman, and says “It is ill dealing with such a foe: he is a wizard both cunning and dwimmer-crafty, having many disguises.”
I’ve looked up “dwimmer” in the OED and Webster’s, and searched a number of pages in Google. Tolkien certainly wouldn’t have been familiar with, nor would he have used a word like “do what I mean”. Am I missing something obvious, here? I can’t even figure out the root of the word.