Automated vulnerability searching tools have led to a dramatic increase of the rate at which such flaws are discovered. One particular searching technique is fault injection i.e. insertion of random data into input files, buffers or protocol packets, combined with a systematic monitoring of memory violations. Even if these tools allow to uncover a lot of vulnerabilities, they are still very primitive; despite their poor efficiency, they are useful because of the very high density of such vulnerabilities in modern software. This paper presents an innovative buffer overflow uncovering technique, which uses a more thorough and reliable approach. This technique, called: Fuzzing by Weighting Attacks with Markers, is a specialized kind of fault injection, which does not need source code or special compilation for the monitored program. As a proof of concept of the efficiency of this technique, a tool called Autodafe has been developed. It allows to detect automatically an impressive number of buffer overflow vulnerabilities.