Abstract. Tweakable blockciphers, first formalized by Liskov, Rivest, and Wagner [13], are blockciphers with an additional input, the tweak, which allows for variability. An open problem proposed by Liskov et al. is how to construct tweakable blockciphers without using a pre-existing blockcipher. This problem has yet to receive any significant study. There are many natural questions in this area: is it significantly more efficient to incorporate a tweak directly? How do direct constructions compare to existing techniques? Are these direct constructions optimal and for what levels of security? How large of a tweak can be securely added? In this work, we address these questions for Luby-Rackoff blockciphers. We show that tweakable blockciphers can be created directly from Feistel ciphers, and in some cases show that direct constructions of tweakable blockciphers are more efficient than previously known constructions. 1