Ribosome-mediated transcriptional attenuation mechanisms are commonly used to control amino acid biosynthetic operons in bacteria. The mRNA leader of such an operon contains an open reading frame with regulatory codons, cognate to the amino acid that is synthesized by the enzymes encoded by the operon. When the amino acid is in short supply, translation of the regulatory codons is slow, which allows transcription to continue into the structural genes of the operon. When amino acid supply is in excess, translation of regulatory codons is rapid, which leads to termination of transcription. We use a discrete master equation approach to formulate a probabilistic model for the positioning of the RNA polymerase and the ribosome in the attenuator leader sequence. The model describes how the current rate of amino acid supply compared to the demand in protein synthesis (signal) determines the expression of the amino acid biosynthetic operon (response). The focus of our analysis is on the sensitivity of operon expression to a change in the amino acid supply. We show that attenuation of transcription can be hyper-sensitive for two main reasons. The first is that its response depends on the outcome of a race between two multi-step mechanisms with synchronized starts: transcription of the leader of the operon, and translation of its regulatory codons. The relative change in the probability that transcription is aborted (attenuated) can therefore be much larger than the relative change in the time it takes for the ribosome to read a regulatory codon. The second is that the general usage frequencies of codons of the type used in attenuation control are small. A small percentage decrease in the rate of supply of the controlled amino acid can therefore lead to a much larger percentage decrease in the rate of reading a regulatory codon. We show that high sensitivity further requires a particular choice of regulatory codon among several synonymous codons for the same amino acid. We demonstrate the importance of a high fraction of regulatory codons in the control region. Finally, our integrated model explains how differences in leader sequence design of the trp and his operons of Escherichia coli and Salmonella typhimurium lead to high basal expression and low sensitivity in the former case, and to large dynamic range and high sensitivity in the latter. The model clarifies how mechanistic and systems biological aspects of the attenuation mechanism contribute to its overall sensitivity. It also explains structural differences between the leader sequences of the trp and his operons in terms of their different functions.