Eukaryotic cells respond to cellular stresses by the inhibition of translation and the accumulation of mRNAs in cytoplasmic RNA–protein (ribonucleoprotein) granules termed stress granules and P-bodies. An unresolved issue is how different stresses affect formation of messenger RNP (mRNP) granules. In the present study, we examine how sodium azide (NaN3), which inhibits mitochondrial respiration, affects formation of mRNP granules as compared with glucose deprivation in budding yeast. We observed that NaN3 treatment inhibits translation and triggers formation of P-bodies and stress granules. The composition of stress granules induced by NaN3 differs from that of glucose-deprived cells by containing eukaryotic initiation factor (eIF)3, eIF4A/B, eIF5B and eIF1A proteins, and by lacking the heterogeneous nuclear RNP (hnRNP) protein Hrp1. Moreover, in contrast with glucose-deprived stress granules, NaN3-triggered stress granules show different assembly rules, form faster and independently from P-bodies and dock or merge with P-bodies over time. Strikingly, addition of NaN3 and glucose deprivation in combination, regardless of the order, always results in stress granules of a glucose deprivation nature, suggesting that both granules share an mRNP remodeling pathway. These results indicate that stress granule assembly, kinetics and composition in yeast can vary in a stress-specific manner, which we suggest reflects different rate-limiting steps in a common mRNP remodeling pathway.