Unbalanced Feistel schemes with expanding functions are used to construct pseudo-random permutations from kn bits to kn bits by using random functions from n bits to (k-1)n bits. At each round, all the bits except n bits are changed by using a function that depends only on these n bits. Jutla investigated such schemes, which he denotes by F^d_k, where d is the number of rounds. In this paper, we describe novel Known Plaintext Attacks (KPA) and Non-Adaptive Chosen Plaintext Attacks (CPA-1) against these schemes. With these attacks we will often be able to improve the results of Jutla.