The Mongols crafted a weapon and style with these limitations in mind: they made their bows much shorter, and in a recurve fashion to offset the loss of power.
The smaller bows also allowed archers to fire while moving, and they were particularly deadly on horseback. The bowstring was drawn with the thumb, and fired from chest level, creating a more “intuitive” style of shooting.
The ancient Chinese were so taken by this practice that it eventually was adopted by their militaries. Sadly, around the turn of the 20th century, the practice was nearly lost as China modernized.