Two approaches to correct for mass discrimination effects associated with Cu and Zn isotopic measurements on two different MC-ICP-MS instruments (a Micromass IsoProbe and a VG Axiom) have been compared and assessed in detail: (1) sample-standard bracketing (SSB), and (2) the ‘empirical external normalisation’ (EEN) whereby a second element is used to simultaneously correct for mass discrimination. This has provided new insights into the mass discrimination behaviours of Cu and Zn under varying instrumental set-ups, and has allowed improvements to be made to the existing correction procedures. With the SSB approach, mass bias stability is a prerequisite, and matrix components must be removed from the analyte to avoid matrix-related mass discrimination effects. By comparison, the EEN approach requires a degree of mass bias instability, and automatically corrects for matrix-related mass discrimination effects. The EEN correction may therefore appear more robust. However, while the EEN correction yields high-precision 65Cu/63Cu and 66Zn/64Zn data, an as yet unidentified source of systematic drift in the 67Zn and 68Zn signals through time hinders analyses of ratios incorporating these isotopes. Using the EEN correction where analyte and spike ratios were measured sequentially within a peak-switching protocol led to a three-fold deterioration in precision relative to static measurements. This is consistent with mass bias drift on the scale of a single five-second-measurement integration. For relative 65Cu/63Cu and 66Zn/64Zn ratio measurements, the SSB and EEN corrections give long-term reproducibilities of less then ±0.07‰ (2SD) for pure Cu and Zn reagents. This is sufficient for resolving mass-dependent isotopic variability in natural and anthropogenic materials.