At the recommendation of the lactation specialist, we bought a Moby Wrap. That's wrap, not to be confused with Moby rap, the electronica/house/club artist from the late 90's/early 00's.
It's a single strip of cloth that can be twisted and contorted around one's body to create a carrying vessel. Extremely comfortable for both carrier and passenger, as you can see.
And it's hands-free!