Kote-Men: How do I do this?

A very nice Waza is Kote-Men and in the last several training lessons I improved a lot not knowing even why. As far as I can analyse it my hip and feet move much faster forward while my arms and shoulder are more relaxed making the complete sequence of two strikes and two steps much faster. The keypoints I want to look at the next training:

• relaxed shoulder and arms
• left leg is relaxed but ready for a move and under tense
• the left leg is straight to activate the movement as fast as possible
• the hip pushes the body forward
• the left leg must move insanely fast forward to start the second step and Men-Strike

I need to get all those points of my movement under better control, because it affects a lot of other techniques too. I.e. the fast switch of relaxing and tensing the left leg is very important for a pure Men-Strike and the Zanshin afterwards.