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we must prioritize the impediments, and keep removing or reducing the top one until velocity is doubled

Hint: We might want to prioritize the impediments by how much the removal/reduction will increase velocity. 25% here, 30% there; pretty soon you're talking a real increase in velocity.

Hint: Improving quality and reducing technical debt are almost always important keys to seriously increased velocity. Not the only keys, but very important.

Velocity is best used for long term planning. I can look at my velocity over several iterations and come up with an average (Preferably a range.) Then I can use that information to say things like: 1) Given the current backlog, how many iterations is it likely to take to complete a given set of stories? 2) How many story points, and by extension what set of prioritized stories, can I deliver by date X (e.g. in time for the trade show?)

I am very wary of anyone who suggests increasing velocity is a goal. *They are just estimates*. It is so easy to game. I've seen it happen both consciously and subconsciously with very undesirable effects.

The only measure of increased productivity is completed work. Measuring this also has the desirable side effect of encouraging people to break work down into the smallest possible deliverable units.