Faster way to mate K+Q vs K

I've been playing around with the tablebases available online and for download and have found a pattern in the way these databases checkmate in K+Q vs K. They do not use the "box" method, instead they follow the following rules (most of the time):

1. Try to keep the queen at a knight's move away from the enemy king.

2. Keep the king a knights move away from the enemy king or directly opposing the enemy king.

3. Use the queen to "herd" the enemy king into your king or a wall, then run it into a wall, where it it will be checkmated.

4. Checks are given rarely, usually on the first move, or a move the pushes back the king.

Here is an example (it is in puzzle form, try them first before clicking "solution" ):

Example 1: (hint: look for the less obvious checkmate!)

And now here is the checkmate using the traditional "box method":

I've never heard of the "box" method. What I usually do is similar to the computers approach (except for that first move up there).

hmmm... interesting...

you see, when I was little, I figured out that the king MUST retreat in the prescence of the queen, so I pushed the king into a corner, then marched my king over there.

for example:

"The mate (K+Q vs Q) can be forced in at most ten moves from any position..."

GM Fine, Basic Chess Endings, p. 1

You can decide on a box, circular, parabolic or any other method you like here as far as I'm concerned as long as you can do it in say, the amount of time it takes to hit the clock each move once you get down to a K+Q vs K position.

Except in Tactics Trainer