DOT orders can be cancelled, but not electronically. it is not cancelled at the push of a button. Entering 'cancel' notifies the specialist of your intent to cancel your order. Sometimes the result is immediate (as if he has set his DOT machine up to allow it). He has at least a minute before he has to do anything about it, maybe two (have never really gotten a straight answer on this one).
NX orders go to the book like plain old DOT orders if the bid AND/OR offer size is 1. Apparently they cease to be 'ecn' orders in that case.
If he feels like it, he can cancel your order.
On NX orders, if there is stock at your price and you're first in line, you probably won't have time to cancel. However, if you get a partial fill you have a good chance of getting the 'out' on the balance if you're quick.
It seems that since the unexecuted portion of the order goes to the book and is subject to the specialists normal handling of such orders on cancellation, I shouldn't notice a quicker cancel on the balance, but I do, sometimes. At least it seems that way...
Hitting the 'cancel' button on DOT orders is like raising your hand in a very crowded classroom to ask a very stingy teacher for a bathroom pass.
NX orders go to the book (like any other order) if the bid OR offer size is 1. In other words, the ecn ceases to exist in that case. Ever notice how often those one's show up? It seems to work hand in hand with 'pennying' to give the specialist more room to play his hand.
Also, NX ceases to function 1 minute before the close. NX is not available if the quote is 'non firm,' whatever that means. Seems like most quotes are that way to me.
Given that the probabilities are that a NX will become just another order on the book, it seems like one practical function of NX is to draw in orders, sort of like a 'loss leader.' So what is purportedly done for the benefit of the public is ultimately for the benefit of the practitioner.
Some very limited PR:
http://www.nyse.com/pdfs/nysedirect.pdf