There is a recent paper by Hoang, Morris & Rogaway which proposes an alternative construction of PRPs from PRFs.
Viet Tung Hoang, Ben Morris, Phillip Rogaway, An Enciphering Scheme Based on a Card Shuﬄe, CRYPTO 2012
The construction has a few nice features.
First, the domain of the PRF is preserved, which is one of your requirements. Second, it provides security beyond the birthday bound. The construction is still quite simple, but the tradeoff compared to Luby-Rackoff is an increase in the number of rounds (logarithmic).
You can see the slides & video of the associated talk at the CRYPTO 2012 program page.
edit: Hm, actually this construction uses a one-bit PRF to build a PRP. Still, you could think of an $n$-bit PRF as $n$ distinct 1-bit PRFs, and use a different bit for each round of this construction. Certainly $n$ rounds would be plenty. Also, you have $n$ distinct 1-bit PRFs that are all keyed by the same key. So your key size would not increase going from PRF to PRP (as it does in Luby-Rackoff -- you need independent keys for each round of the Feistel network).