Can REM Sleep Make You Tall?

Mr. Tall spent last night in the hospital doing a sleep study. You know – where they hook dozens of probes up to you and then expect you to sleep deeply so they can monitor you. Right!
Anyway, he had a conversation with the tech guy about kids and how some of our kids sleep deeply, but others are light sleepers.
The sleep tech said that you need to get into a deep REM sleep stage in order to grow as that is when your body does all of its’ growing. I found this interesting as I sleep so well that an earthquake couldn’t wake me at times.
I must have done a ton of REM sleeping as a kid and during puberity. So I told Mr. Tall that from now on, he needs to wake me every hour so I don’t have a chance to enter into REM sleep as I don’t want to grow any taller at this point.