Phenomenological approaches to quantum gravity implement a  minimum resolvable length-scale but do not link it to an underlying formalism  describing geometric superpositions. Here, we introduce an intuitive approach in  which points in the classical spatial background are delocalised, or ``smeared",  giving rise to an entangled superposition of geometries. The model uses  additional degrees of freedom to parameterise the superposed classical  backgrounds. Our formalism contains both minimumlength and  minimummomentumresolutions and we naturally identify the former with the Planck  length. In addition, we argue that the minimummomentumis determined by the de  Sitter scale, and may be identified with the effects of dark energy in the form  of a cosmological constant. Within the new formalism, we obtain both the  Generalised Uncertainty Principle (GUP) and Extended Uncertainty Principle  (EUP), which may be combined to give an uncertainty relation that is symmetric  in position and momentum. Crucially, our approach does not imply a significant  modification of the position-momentum commutator, which remains proportional to  the identity matrix. It therefore yields generalised uncertainty relations  without violating the Equivalence Principle, in contradistinction to existing  models based on nonlinear dispersion relations. Implications for cosmology and  the black hole uncertainty principle correspondence are briefly discussed, and  prospects for future work on the smeared-space model are outlined.