The NICE test for auxiliary verbs

So I was flipping through a book on linguistics yesterday (typical bathroom reading, y'know....) and I came across an interesting memory trick that might help you remember the difference between "normal" verbs and auxiliary verbs.

What are the most important differences between "normal" and auxiliary verbs? Think of the NICE test:

• Both time and modal auxiliary verbs have NEGATIVE forms: hadn't, wouldn't couldn't, isn't, aren't (NOT: amn't.) 
• For questions, the order of auxiliary verbs can be INVERTED: he had = had he?; they could = could they?
• You can have them in shortened forms as long as you know what the CONTEXT is: "They could go there by car, couldn't they?" -- "They could." (The sentence doesn't make any sense if you don't have the question before it. 
• You couldn't do this with "You like running, don't you?" -- "I like.")
• They can be stressed with EMPHASIS: "You can't do this." -- "I can!!" 

(EDIT: Oh, and remember: You can't use two auxiliary verbs together: I will can go, He did must speak.)

(Source: The Oxford Concise Dictionary of Linguistics, by P. H. Matthews)