I hope someone has already made this suggestion, but doubtlessly it is buried within a host of other suggestions.  I feel that the following idea, however, deserves a post devoted to nothing but the idea itself.  I think this will go a long way to both making tactical combat "quicker," but more entertaining as well.

Instead of the current system whereupon you move a unit 1 by 1 during your turn, waiting painfully for the animations to finish before you can do anything else, why not set orders for your units beforehand and then hit a "execute" button to carry them out?  Instead of every animation happening one by one, you could see everything happen at once, giving a feeling of "true combat" to the bloody affair.

In addition to saving a lot of the player's time whilst looking pleasing to the eye, this would add an additional layer of strategy to the game:

example: "Do you commit 3 units to attack the demon, or just rely on 1 plus your mage's spell?"

In other words, if you overcommit units to an enemy's death, you can possibly waste actions.  It will, in one stroke, improve tactical depth *and* make tactical battles far more streamlined without changing any of the actual mechanics of the combat system itself.

A lot of games have done this in the past to great success!

At the very least, let us order more than one unit at a time so we don't have to wait for the animations to end before making the next order!  I like watching the animations, so I don't want them turned off, but man is it painful to sit through them one at a time...