So what kind of "Deal" did Elena make with Elijah to get Stef out of the tomb?

Was it not something like this:

Elijah wanted to actually keep Elena safe to lure Klaus out so he could kill him.
Elena was going out on like suiscide missions to protect the ones she loved.
So, Elijah said, she was to do nothing and he would kill Klaus.
Elena was like, only if you get Stefan out of the tomb.
I think that was about it.