What are some things you do to improve your speed across the pen? Particularly between barrels 1 & 2. 

This is good question and I hope you get some more answers. BUMP

I like to get mine “Smooch Broke” so when I smooch to them, they really hustle, but I still struggle to get one freed up across the pen while running in a small indoor.

Kick?

I suppose it depends exactly where you are needing to pick up time.

Is it really your speed across the pen, or is your horse not FIRING out of the first barrel turn?

Or are they rating too soon for the second, and costing you time there?

Maybe more to it than just the speed in-between.

And if your 2nd to 3rd barrel is fine, what is going correct there that is not between 1st and 2nd? (Lots to analyze!)

Honestly for me it is getting a good first barrel.  That is where I start my homework if I am slow getting across the pen.