Limiting h.264 VBR Peaks in FMLE

Hey, I'm currently streaming out content with large amounts of static image/little motion and then moments of rapid motion/moving image (1 minute of movement for every 5 of static shots, give or take)

Using h.264 VBR with this content gives peaks of bitrate way too high for our application, with a 450kbps stream peaking at 1.2mbps when the almost static content switches over to the fast moving video

Is there any method by which H.264 VBR can be limited in FMLE? What codec does FMLE use for h.264 encoding?

Thanks!