What prompts you to "try to add speed"?
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Nothing prompts me during the draw other than a conscious effort to reduce my draw time. I'm using Steve Anderson's book, which recommends you do sets - i.e. 10 warm ups, 10 at your normal par, and then try to do a set below par. As I try to do the last sub par set, my grip pressure tends to go from neutral and floating, towards the white knuckle death grip.
In general, what's prompting me to try and add speed is I've noticed a lull in my overall improvement and a bit of burnout. I'm trying new drills and experimenting with different things - i.e. steel matches, USPSA matches, etc. (I've shot IDPA for years). I want to see if with enough reps I can make myself a bit speed blind, which will hopefully let me see what I need to faster.