The compression behaviours of La2NiO4+δ and Pr2NiO4+δ have been studied up to a pressure of 2.8 and 2.2 GPa respectively. Using neutron diffraction, the mechanism of compression, and the behaviour of the NiO6 and La/PrO9 polyhedra in these layered perovskite materials have been determined. Their compression mechanisms have then been compared to related materials (La2-xPrxNiO4, Pr2-xNdxNiO4, La2-xSrxNiO4 and Pr2-xCaxNiO4) where the unit-cell volume has been reduced by controlling the composition (x), which acts as an 'effective chemical pressure'. Understanding the effects of both has implications for materials design; pressure can be used to finely tune a property, which theoretically may then be emulated using chemical doping.