Easton Jazz Superlight 1214s fit your description.
I made up some arrows for my granddaughter's little MadDog bow. Her bow is rated at 22# @ 24", so to make sure some adult doesn't over-draw the bow, I cut the arrows to 24". If I anchor with the heel of my hand on the point of my chin, I can shoot groups as tight at 7 yards as I can from my big bows.
With 3 2" feathers and the 60 or so grain points that came with them, these things are surprisingly fast. She is probably only drawing about 16 - 18 #, but loves shooting it and both bow and arrows will grow with her for a couple more years.