It is known that given a directed graph E and a Subset X of vertices, the sum Sigma(v epsilon X) P-v, of vertex projections in the C*-algebra of E converges (strictly, in the multiplier algebra) to a projection P-X. Here we give a construction which, in certain cases, produces a directed graph F such that C*(F) is isomorphic to the corner PXC*(E) P-X. Corners of this type arise nawrally as the fixed-point algebras of discrete coactions on graph algebras related to labellings. We prove this fact, and show that our construction is applicable to such a case whenever the labelling satisfies an analogue of Kirchhoff's voltage law.