Stochastic effects in gene expression may result in different physiological states of individual cells, with consequences for pathogen survival and artificial gene network design. We studied the contributions of a regulatory factor to gene expression noise in four basic mechanisms of negative gene expression control: 1), transcriptional regulation by a protein repressor, 2), translational repression by a protein; 3), transcriptional repression by RNA; and 4), RNA interference with the translation. We investigated a general model of a two-gene network, using the chemical master equation and a moment generating function approach. We compared the expression noise of genes with the same effective transcription and translation initiation rates resulting from the action of different repressors, whereas previous studies compared the noise of genes with the same mean expression level but different initiation rates. Our results show that translational repression results in a higher noise than repression on the promoter level, and that this relationship does not depend on quantitative parameter values. We also show that regulation of protein degradation contributes more noise than regulated degradation of mRNA. These are unexpected results, because previous investigations suggested that translational regulation is more accurate. The relative magnitude of the noise introduced by protein and RNA repressors depends on the protein and mRNA degradation rates, and we derived expressions for the threshold below which the noise introduced by a protein repressor is higher than the noise introduced by an RNA repressor.