The following essay was recommended to me by Paul Draper. The paper is not a defense of the fine-tuning argument, but he regards it as one of the best critiques of the many worlds explanation of fine-tuning:

Roger White, “Fine-tuning and Multiple Universes,” forthcoming in Nous
ftmu.pdf (PDF)

Here is some info about the author:

ROGER WHITE, (Ph.D., MIT), Assistant Professor of Philosophy, specializes in philosophy of science, epistemology, and metaphysics. He is currently focusing on epistemological issues in the philosophy of science, particularly those having to do with probability and explanation. His main interests in metaphysics concern matters of identity and essential properties. He is the author of “Fine-tuning and Multiple Universes” (Nous).