Coupling the control of expression stochasticity (noise) with the capacity to expression change (plasticity) can constrain gene function and limit adaptation. Which factors contribute then to modulate this coupling? Transcription re-initiation is generally associated with coupling and this is commonly related to strong chromatin regulation. We alternatively show how strong regulation can however lead to plasticity uncorrelated to noise. The character of the regulation is also relevant, with plastic but noiseless genes usually subjected to broad expression activation whereas plastic and noisy genes experience targeted repression. This differential action is similarly noticed in how histones influence these genes. In contrast, we find that translational mechanisms are the ones separating noise from plasticity in low-plastic genes, a pattern associated with the simplicity of their expression regulation. Neighboring genome architecture as modifier appears then only effective in highly plastic genes. This poses ultimately an interesting paradox between intergenic distances and modulation, with short intergenic distances both associated and not associated with noise at different plasticity levels. Balancing the coupling among different types of expression variability appears thus as a potential shaping force of genome architecture and regulation