Electrostatic shocks observed previously on the S3-3 satellite all have electric fields primarily perpendicular to the magnetic field, while the double layers observed in the laboratory and in computer simulations generally involve a mode whose electric field would be parallel to the magnetic field in the magnetized case. Since parallel potentials are known to exist in association with the perpendicular shocks, electric field data from the S3-3 satellite were searched for mostly parallel fields of hundreds of millivolts per meter. The data set consisted of auroral zone passes containing 207 perpendicular shocks, which were used in previous statistical studies, plus 40 additional orbitss. At most a few events were found. Hence upper limits are placed on the number and size of double layer structures associated with perpendicular shocks. For most reasonable sets of parameters, the double layer structures cannot be greater than roughly 3 km in latitudinal extent when mapped to the ionosphere.