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The behaviour of materials under spatial confinement is sensitively dependent on the nature of the confining boundaries. In two dimensions, confinement within a hard circular boundary inhibits the hexagonal ordering observed in bulk systems at high density. Using colloidal experiments and Monte Carlo simulations, we investigate two model systems of quasi hard discs under circularly symmetric confinement. The first system employs an adaptive circular boundary, defined experimentally using holographic optical tweezers. We show that deformation of this boundary allows, and indeed is required for, hexagonal ordering in the confined system. The second system employs a circularly symmetric optical potential to confine particles without a physical boundary. We show that, in the absence of a curved wall, near perfect hexagonal ordering is possible. We propose that the degree to which hexagonal ordering is suppressed by a curved boundary is determined by the "strictness" of that wall.