In 1966, the Gemini XI crew set an as-of-yet unbroken altitude record within low Earth orbital flights. Using the Agena's engine, Pete Conrad and Dick Gordon reached an apogee (peak distance from the Earth) of 850 miles; most Gemini missions, and missions since, have operated under the 200 mile altitude. So why did Gemini XI get to fly higher than any other mission? In short, because Conrad wanted to. Two old archives on Vintage Space give the long answer, one digging into the high-flying Gemini XI flight and the other the lunar Gemini mission proposal that spawned it.