Observations of 12 compact extragalactic sources were made at 2695 and 8085 MHz in order to detect weak intensity fluctuations caused by interstellar scintillation. Pulsar data are used to estimate the parameters of the interstellar medium needed to interpret the measured upper limits in terms of source angular diameters which are much larger than the scintillation cutoff diameter. It is shown that the observed source rms brightness temperatures are less than 10 to the 15th K and 10 to the 14th K at 2695 and 8085 MHz, respectively, making self-absorbed proton-synchroton radiation and high-brightness coherent mechanisms unlikely. If the sources are composed of 'point' components, each source can contain no fewer than 10,000 such components.