The defining characteristic of the superconducting state is its ability to carry electrical currents without loss, The process by which it does this has been extensively studied for decades but there are still many unresolved issues; In particular, the critical current, which is the maximum electrical current that a superconductor can carry without loss, remains a poorly understood concept at the microscopic level. In a type II superconductor, a flux-Line lattice (FLL) forms if a magnetic field between H-cl and H-c2, the lower and upper critical fields, is applied : flowing electrical currents will exert a force on this PLL. If the FLL remains pinned, the current flows without loss of energy and the effective resistance remains zero. However, if the lattice moves in response to the current, energy is dissipated and the zero-resistance state is lost. Because of its relevance to the critical cru rent, the types of structures that these moving lattices can form have attracted much recent theoretical attention(1-4). Here we report magnetic decoration studies of flowing vortex lattices which show evidence for a transition, as a function of increasing flux density, from a layered (or smectic) FLL2 to a more well-ordered moving Bragg glass(1).