Various results show that oblivious transfer can be implemented using the assumption of noisy channels. Unfortunately, this assumption is not as weak as one might think, because in a cryptographic setting, these noisy channels must satisfy very strong security requirements. Unfair noisy channels, introduced by Damg?ard, Kilian and Salvail [Eurocrypt '99], reduce these limitations: They give the adversary an unfair advantage over the honest player, and therefore weaken the security requirements on the noisy channel. However, this model still has many shortcomings: For example, the adversary's advantage is only allowed to have a very special form, and no error is allowed in the implementation. In this paper we generalize the idea of unfair noisy channels. We introduce two new models of cryptographic noisy channels that we call the weak erasure channel and the weak binary symmetric channel, and show how they can be used to implement oblivious transfer. Our models are more gener...