What makes a puzzle hard–III (Puzzle No. 3,311)

I think one of the unheralded keys to solving a crossword, cryptic or otherwise, is the intersecting letters.  Sometimes letter patterns are enough to get an answer; often they are sufficient to narrow down the possible answers from the definition down to a single correct one.  Since we do a lot of this intutitively (see Aunt Minnie), we don't pay a lot of attention to that tool.  

In cryptics, intersecting letters are great because they greatly reduce the number of anagram possibilities.  A seven-letter anagram has 7! (factorial: a math term) or 5,040 possibilities.  Get the four intersecting letters, and there are only three left to place: just six possibilities.  You can roll each of them around in your mind or on a piece of paper and get the answer by trial and error.  

Intersections are also a big reason why variety cryptics tend to be harder than straight ones.  Let's look at two examples. 

The latest Harper's puzzle (prize puzzle, so no hints please) has 12 unclued entries.  So a lot of the intersecting words won't be filled in the first time you run through the puzzle and the clued entries will be harder.  You can't do anything with the unclued answers until you get enough intersecting normal answers to get two or three theme answers solely from intersecting letters.  But then once you have those, the rest of the theme answers come in in a hurry.  

Another type of variety cryptic alters the entries before they go in the grid.  In that case while you might get a possible entry from the intersecting letters, you then have to back-transform it (another math term) into the definition and wordplay as given in the clue.  Sometimes that's the key to cracking the alteration instructions.  

The Nation cryptic No. 3,311 

Link to puzzle: http://www.thenation.com/article/178019/puzzle-no-3311

Degree of difficulty (by standards of this weekly puzzle): easy

Hozom’s comment: The Short and Long of It, in which Hot and Trazom share some of their favorite three-word clues and point out that charade clues and double definitions do not need an indicator. Playing with the spacing (i.e. removing the space between words in a clue) can let you create two- and one-word clues that still have the essentials of definition, indicator (if necessary), and wordplay. Exclamation point clues (those where the definition incorporates the wordplay or vice versa) also lead to brevity.