Protein noise measurements are increasingly used to elucidate biophysical parameters. Unfortunately noise analyses are often at odds with directly measured parameters. Here we show that these inconsistencies arise from two problematic analytical choices: (i) the assumption that protein translation rate is invariant for different proteins of different abundances, which has inadvertently led to (ii) the assumption that a large constitutive extrinsic noise sets the low noise limit in gene expression. While growing evidence suggests that transcriptional bursting may set the low noise limit, variability in translational bursting has been largely ignored. We show that genome-wide systematic variation in translational efficiency can-and in the case of E. coli does-control the low noise limit in gene expression. Therefore constitutive extrinsic noise is small and only plays a role in the absence of a systematic variation in translational efficiency. These results show the existence of two distinct expression noise patterns: (1) a global noise floor uniformly imposed on all genes by expression bursting; and (2) high noise distributed to only a select group of genes.