Double-walled carbon nanotubes are needed in a pure, highly crystalline form before features such as their electronic properties, thermal transport and mechanical behaviour can be investigated. Here we fabricate a paper-like material that consists of hexagonally packed bundles of clean, coaxial carbon nanotubes whose double walls vary little in diameter; it is prepared in high yields using chemical-vapour deposition with a conditioning catalyst and two-step purification. Our results will enable investigation of the physical properties of double-walled carbon nanotubes, which are predicted to be superior to those of both their single- and multiwalled relatives.