We explored how transcriptional noise propagates in gene-regulatory pathways by studying the induction of two downstream genes by transcription factors c-fos and c-jun. They are produced for a brief period following serum stimulation of cells and then activate the promoters of their target genes by binding to them as heterodimers. We found that, even though they are coordinately expressed at the population level, in individual cells the expression of c-fos and c-jun is noisy and uncorrelated with each other. The expression of the downstream genes is also noisy, but there is little or no effect of the noise in the upstream genes on the expression of the downstream genes. The noise is not transmitted, because the number of heterodimers present in single cells is relatively invariant, and the induction of downstream genes is insensitive to the number of heterodimers in individual cells. Sequestration of promoters of the downstream genes within compact chromatin is a likely cause of this insensitivity. These barriers to the propagation and amplification of noise are likely to be commonplace in higher eukaryotes.