The last space shuttle flight has smallest space shuttle crew because it's the last space shuttle flight. Bear with me, that's not a trick answer.
Since the loss of Columbia in 2003, NASA has strictly required a Launch On Need (LON) parallel mission for every shuttle flight. Put more simply, every time a shuttle flies, another shuttle is prepped on standby for an orbital rescue mission, should the primary shuttle suffer damage during launch that prevents it from safely returning to Earth.
STS-135 was originally STS-335, the Launch On Need standby flight for STS-134, the final flight of Endeavour that was intended to be the last shuttle mission. As NASA had already spent the money getting Atlantis flight-worthy, they convinced Congress to backdoor STS-335 into STS-135 — provided Endeavour didn't need a rescue during its final flight. When Endeavour landed safely on June 1, 2011, STS-135 was finally, officially a go.
However, as both Discovery and Endeavour have been retired, there is no rescue shuttle on standby for STS-135. The Launch On Need plan for Atlantis involves not one, but a pair of three-man Russian Soyuz capsules, which can rescue two shuttle astronauts apiece with the help of each capsule's respective pilot.
Requiring two LON craft is a daunting enough prospect, but flying Atlantis with a standard 6-man crew would require a logistically staggering triple-Soyuz Launch On Need mission. That was a non-starter for greenlighting STS-135, so the Atlantis mission profile was developed for a modern minimum four-man crew. (Only the first four shuttle flights, all shakedown missions for Columbia, included two-man crews. No shuttle has ever flown with a three-man complement.)
That's not just a scientifically sagacious skeleton crew, it's a fundamentally unforgettable return flight for Geek Trivia.
The quibble of the week
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Jay Garmon has a vast and terrifying knowledge of all things obscure, obtuse, and irrelevant. One day, he hopes to write science fiction, but for now he'll settle for something stranger — amusing and abusing IT pros. Read his full profile. You can also follow him on his personal blog.