I am going to hijack Jens thread a little here.
Chip uses a super that is referred to as 3/4 depth although it is actually a 4/5 depth when compared to a deep.
HISTORY LESSON.
Back in 1852 when Langstroth invented and patented his removable frame hive with the frames being removed from the top, verses some of the European designs of the period that removed the frames from the side. He used standard dimension lumber in his hive design. At that time and up until the early 1960 the dressed size of a 1X10 was 7/8" X 9 5/8". In his quest to provide the perfect manageable size hive to meet the needs of the bees and the beekeeper, he settled on a design of 2 - 10 frame, 9 5/8" deep supers. To this day his size space requirement for the bees have remained unchanged. In 1862 Charles Dadant was trying to improve on Langstroth's hive design and trying to keep the bees in a single brood super, His design was a single 12 frame 11 5/8" super made from a standard 1X12 of the time. Dadant's jumbo super size never caught on, although jumbo size foundation was available and stocked by bee supply stores into the 1990's. Both the 7 5/8" and the shallow 5 11/16" supers used standard width lumber at the time so were obvious choices for super sizes. The problem with these sizes. There wasn't that much of a difference in weight with the 7 5/8" super. And the 5 11/16" was to small and requires twice as many supers. Dadant's 6 5/8 was introduced into beekeeping between 1921 - 1946 when Charles 3 sons had taken over the company. The 6 5/8 super was a special custom size with 3 Dadant's equaling the height of 2 of Langstrothe's deeps. It has become the leading standard super for honey storage and is also becoming widely used for brood supers as well amongst the hobbyist and older beekeepers with bad backs. With the new standards in lumber widths now a 1X10 is dressed to 9 1/2" and with additional shrinkage after planing the boards can end up being only 9 1/4" wide. Do to this, lumber of the next width needs to be purchased so it can be ripped down to the desired size, or the lumber special ordered custom milled to the desired super size specification.
In the last 10 years the 8 frame super is becoming more popularity with the new beekeeper thus also reducing super weigh. These can presents more of a challenge as the brood chamber can become congested faster and sooner, and more beekeeper manipulation may be needed.