"do it yourself" acoustics

13 by 13 is tough since the same frequencies are reinforced and cancelled by two of your three dimensions. If you can move the system to a different room, you'll definately be better off. If you have 8 foot ceilings, you will get artificially strong bass at 44, 87, 130, 174, 217, and 261 Hz with big gaps inbetween. Bass below 44 Hz will be hard to come by. That's tough to correct. You may need to either get a very narrow bandwidth equalizer or go to the Rives website and look into that equipment.

Full bookshelves on side walls - both, to get rid of the squareness or your room?

Agree with Ozfly that active room correction is the way to go. Suggest you also look at TacT's room correction units.
FYI, they recently lowered their pricing via direct sales.

That speaker and your dimensions are the poster child for our PARC. I don't normally post something that strong about our products--but in this case it's just the truth. Ozfly already mentioned it. In the other areas--absorption and diffusion, be sure to check out our resource section--there's lots of free advice and articles there that may help you.

Rives Audio

I am in a similar situation. I have 12 by 12 room and the squareness(is this a word?) is the killer here. I've had some success in making it work.

1) If this is a dedicated listening room and you can do it, position the speakers at 90 degrees (in other words make a diamond shape rather than a square) this is the best thing you can do to improve sound in your square room.

2) if you have bass issues, bass traps DIY or pay a pile of money for commercial ones. My bass it solid, not over powering so I removed my DIY traps which worked too good.

3) Flutter echo

4) 1st reflection points, don't forget the 1st reflection points on the ceiling and back wall.

Flutter echo made my room very bright, also I put acoustic foam in the corners.

Hope that helps. My room is tolerable.

Rob