Bacterial resistance to antibiotics usually incurs a fitness cost in the absence of selecting drugs, and this cost of resistance plays a key role in the spread of antibiotic resistance in pathogen populations. Costs of resistance have been shown to vary with environmental conditions, but the causes of this variability remain obscure. In this article, we show that the average cost of rifampicin resistance in the pathogenic bacterium Pseudomonas aeruginosa is reduced by the addition of ribosome inhibitors (chloramphenicol or streptomycin) that indirectly constrain transcription rate and therefore reduce demand for RNA polymerase activity. This effect is consistent with predictions from metabolic control theory. We also tested the alternative hypothesis that the observed trend was due to a general effect of environmental quality on the cost of resistance. To do this we measured the fitness of resistant mutants in the presence of other antibiotics (ciprofloxacin and carbenicillin) that have similar effects on bacterial growth rate but bind to different target enzymes (DNA gyrase and penicillin-binding proteins, respectively) and in 41 single-carbon source environments of varying quality. We find no consistent effect of environmental quality on the average cost of resistance in these treatments. These results show that the cost of rifampicin resistance varies with demand for the mutated target enzyme, rather than as a simple function of bacterial growth rate or stress.