We describe a cryptanalytical technique for distinguishing some stream ciphers from a truly random process. Roughly, the ciphers to which this method applies consist of a "non-linear process" (say, akin to a round function in block ciphers), and a "linear process" such as an LFSR (or even fixed tables). The output of the cipher can be the linear sum of both processes. To attack such ciphers, we look for any property of the "non-linear process" that can be distinguished from random. In addition, we look for a linear combination of the linear process that vanishes. We then consider the same linear combination applied to the cipher's output, and try to find traces of the distinguishing property.In this report we analyze two specific "distinguishing properties". One is a linear approximation of the non-linear process, which we demonstrate on the stream cipher SNOW. This attack needs roughly 295 words of output, with work-load of about 2100. The other is a "low-diffusion" attack, that we apply to the cipher Scream-0. The latter attack needs only about 243 bytes of output, using roughly 250 space and 280 time.