Is it possible for my bunnies to sleep in bed with me?

I have 2 beautiful holland lops who I love to death and I'd like for them to start sleeping in bed with me.
First off, I'd like to say I'm 100% sure I won't crush them in my sleep. They're the size of small cats and I used to sleep with my cat when he was a kitten barely larger than my hand. I am very aware of presences in my bed and I don't roll around much.
Also, I sleep by myself in a king size bed and I usually sleep on a certain side. In the other corner, I've placed a litter box that I know I won't knock over. I also purchased a plastic mattress cover in case they have any accidents.
I put their cage on a desk right next to my bed so that they can freely go in and out of the cage as they please. They also will not jump off the bed.
The only thing I'm worried about is their sleep cycle. They get kinda rowdy around 6am and I feel like it might wake me up.
So what do y'all think?
Ive heard of a few stories where this was successful but I just wanted more opinions Thanks :bunnybutt:

My first rabbit, Scone MacBunny, was out of his cage all night, as is my present bunny, Natasha Rabbitova. Natasha will jump in and out of bed as the night progresses - most of the time she'll sleep next to my bed, but it's not uncommon if I get up in the middle of the night to find her snuggled up against my leg on the bed.

It took a while to convince her that even if she was happy and ready for attention at 3AM, Daddy needs his sleep. Now she will only hop up on my pillow and groom my head if she can tell I'm awake. She also has an excellent internal clock, and very often will jump into bed and start kissing me a few minutes before the alarm goes off - especially on weekends, when the alarm isn't actually going to go off and I'd hoped to sleep late...

CUTE! I wish I could sleep with my bunnies, always have, but they are mini and I toss and turn a lot.