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Post-transcriptional regulatory processes may change transcript levels and affect cell-to-cell variability or noise. We study small-RNA downregulation to elucidate its effects on noise in the iron homeostasis network of Escherichia coli. In this network, the small-RNA RyhB undergoes stoichiometric degradation with the transcripts of target genes in response to iron stress. Using single-molecule fluorescence in situ hybridization, we measured transcript numbers of the RyhB-regulated genes sodB and fumA in individual cells as a function of iron deprivation. We observed a monotonic increase of noise with iron stress but no evidence of theoretically predicted, enhanced stoichiometric fluctuations in transcript numbers, nor of bistable behavior in transcript distributions. Direct detection of RyhB in individual cells shows that its noise is much smaller than that of these two targets, when RyhB production is significant. A generalized two-state model of bursty transcription that neglects RyhB fluctuations describes quantitatively the dependence of noise and transcript distributions on iron deprivation, enabling extraction of in vivo RyhB-mediated transcript degradation rates. The transcripts' threshold-linear behavior indicates that the effective in vivo interaction strength between RyhB and its two target transcripts is comparable. Strikingly, the bacterial cell response exhibits Furdependent, switch-like activation instead of a graded response to iron deprivation.