Finite-difference (FD) modelling of seismic waves in the vicinity of dipping interfaces gives rise to artefacts. Examples are phase and amplitude errors, as well as staircase diffractions. Such errors can be reduced in two general ways. In the first approach, the interface can be anti-aliased (i.e. with an anti-aliased step-function, or a lowpass filter). Alternatively, the interface may be replaced with an equivalent medium (i.e. using Schoenberg & Muir (SM) calculus or orthorhombic averaging). We test these strategies in acoustic, elastic isotropic, and elastic anisotropic settings. Computed FD solutions are compared to analytical solutions. We find that in acoustic media, anti-aliasing methods lead to the smallest errors. Conversely, in elastic media, the SM calculus provides the best accuracy. The downside of the SM calculus is that it requires an anisotropic FD solver even to model an interface between two isotropic materials. As a result, the computational cost increases compared to when using isotropic FD solvers. However, since coarser grid spacings can be used to represent the dipping interfaces, the two effects (an expensive FD solver on a coarser FD grid) equal out. Hence, the SM calculus can provide an efficient means to reduce errors, also in elastic isotropic media.