With woven wire I'd pull and fasten the top strand first, then work my way down, keeping the strands lined up vertically where I stapled them. That required me to lug a minimum of tools. Then I'd restore tension to all strands by walking along and using two pairs of pliers to tighten the ripples.
Tightening was a leisurely activity. It left a fence so straight that I could I could see from a distance if everything was okay. The ripples allowed stretching if a limb fell on the fence, and the ripples could easily be retightened.