R2K at High Power Rocketry reports on a 38mm minimum diameter rocket, to fly on an L5000. Yes, you're reading that right. A ridiculously high-thrust L motor, in a 38mm rocket.
It's a 68" long custom-made L motor, made by Binder Design. The motor case serves double duty as the aft airframe. It has an aluminium fin can, made of 1/8" metal and brazed together for strength. The fin can will be used more than once; the motor case will not as it's practically destroyed during firing.
The motor itself is incredible. It hits 3000 psi and burns 2600Ns of APCP is just half a second. The grains them selves are 10" long and vacuum cast to better than 99% of theoretical density - any less would invite a CATO. The nozzle has a huge 3/4" opening. Motors with high length-to-diameter ratios are hard to pull off; the builder, Mike F of Binder Design, has spent 10 years testing the motor design. A previous flight with it broke Mach at 350 feet and went to Mach 2 and 18000 feet - despite losing a fin on the way up!
It's simmed to Mach 3 and 30000+ feet. It'll recover on a small x-form chute; there's a tracker in the nose cone.
Here is the thread on Rocketry Planet, if you dare to read 3 pages of cool stuff, and 10 pages of arguing about ridiculously complicated (and cool) motor designs.