Now from the same manufacturer we are pushing modern state of the art battery technology with the lithium battery. This one is physically about the same size as the last one, 6.6” x 5.2” x 6.88", and definitely no problem with storage capacity (they like to use these to power electric and hybrid cars).

The Braille ML30C weighs just 9.3 pounds, can do 1658 Pulse Cranking Amps, has 84-H storage capacity, and no problem with deep discharge. The final kicker is, current price is up to 30 times the price of a conventional lead acid battery (close to $2000-USD). See the manufacturer's web site at:
www.braillebattery.com

Well if it's that powerful, how about a smaller one?

The Braille ML20C weighs just 6.1 pounds, is 6.8” x 3.4” x 6.0", and small enough to put two of them into one original MGA battery tray. It still has 1152 pulse cranking amps, and 48 AH storage capacity. This all sounds very nice, except for the cost (currently nearly $1500-USD). See the manufacturer's web site at:
www.braillebattery.com

There are also:
ML14C - 4.5 pounds - 827 PCA - 42-AH - 5.8” x 3.4” x 5.75” - $1250-USD
ML9C   - 3.7 pounds - 693 PCA - 36-AH - 5.8” x 3.4” x 4.25” - $950-USD
They come smaller yet, but not suitable for storage capacity as an automotive battery. Given enough time the prices should come down some, but don't hold your breath waiting for a $100 battery any time soon.

Addendum October 2013:
In two years time the Pulse Cranking Capacity of these batteries has inceassed significantly, but the price has not come down much yet.