Residual trapped magnetic flux, arising from incomplete Meissner effect, has been studied experimentally in a number of single tantalum-niobium mixed-crystals. In these crystals the periodicity of the lattice potential is partially destroyed by the random occupation of the lattice sites by the two kinds of atom. As a result, the conduction electrons in the normal state have a short mean free path and the crystals exhibit to a marked degree the properties of a `non-ideal' superconductor, such as wide transitions and high critical magnetic fields. It is found, however, that if the crystals are pure there is no detectable trapped flux. This is interpreted as showing that, if flux is to be trapped, there must be sites present which act as barriers to the movement of normal regions, preventing their escape to the surface.