Speed does not come from a single keystroke getting faster. It comes from frequent letter pairs turning into one movement.
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A couple of dozen pairs repeat so often in English that together they make up a large share of any text. Once they are in the hand, only the rare places still need separate practice.
While drilling, do not think of the letters one at a time. Look at the pair as a whole and let the two fingers move almost together.
The drill gives the pairs on their own, with no word around them. You will meet them inside words in the letters drill and in real text.