A typical two-stage process governs the selection of meal items in an Italian menu. The process admits a direct formalization in terms of choice spaces. Path-independent choice spaces are cryptomorphic to convex geometries (or antimatroids, introduced by Robert E. Jamison). There results a construction of a new convex geometry for a convex geometry (the base) given together with a family of convex geometries (the fibers) indexed by the elements of the base; we call the outcome a resolution.