We consider the problem of complete information dissemination among n autonomous processors in a fully connected distributed system. Initially, each processor possesses information not held by any other processor; it is required that all the processors obtain all the information in the shortest possible time. Messages are exchanged in discrete, synchronized rounds; message size is unlimited, but during a round, each processor may transmit messages to, or receive messages from, at most k other processors. We show that Rlogλ(k)n H rounds are necessary for such an information exchange and that Rlogλ(k)n H+3 are sufficient, where λ(k) = (k+√ddddd k+4 )/2. This settles in the affirmative a 10-year-old conjecture of Entringer and Slater; our lower bound is new even for the case k = 1.