At ACISP 2004, Giraud and Knudsen presented the first fault analysis of DSA, ECDSA, XTR-DSA, Schnorr and ElGamal signatures schemes that considered faults affecting one byte. They showed that 2304 faulty signatures would be expected to reduce the number of possible keys to 240, allowing a 160-bit private key to be recovered. In this paper we show that Giraud and Knudsen's fault attack is much more efficient than originally claimed. We prove that 34.3% less faulty signatures are required to recover a private key using the same fault model. We also show that their original way of expressing the fault model under a system of equations can be improved. A more precise expression allows us to obtain another improvement of up to 47.1%, depending on the values of the key byte affected.