The magnetic flux noise generated by films and crystals of Bi2Sr2CaCu2 O8+y and YBa2Cu3 O7-x, up to 30 μm thick and cooled in nominally zero magnetic field, has been measured at opposing surfaces by two dc superconducting quantum interference devices. For both materials, the noise sources at the two surfaces were highly correlated at specific temperatures in a given cooldown. This result suggests that the observed vortices moved as rigid rods. At other temperatures, the noise was mostly uncorrelated, suggesting that the relevant vortices were pinned at more than one point along their length