The basic assumption of the logistic contagion model of cultural transmission is that the rate of adoption of innovations increases with the number of knowledgeable tutors and the number of uninformed observers. To test this assumption, pigeons, Columba livia, were presented with the problem of pecking open a stoppered, inverted test-tube to obtain seeds. In experiment 1, tutor number was increased by presenting caged observers with either one, three, six or nine tutor(s). In experiment 2, the number of uninformed bystanders was increased by adding two, five, eight or no bystanders (pigeons that could not provide demonstrations) to tutor-observer dyads. In experiment 1 the observers learned more quickly with increasing tutor number; both latency of first peck to the test-tube stopper and latency of test-tube opening decreased linearly with increasing tutor number. Increasing tutor number also decreased the latency of the first demonstration within multi-tutored demonstrations, but the latency of the average demonstration increased with tutor number. In experiment 2 observers learned more slowly with increasing number of bystanders; both the latency of first peck to test-tube and the latency of test-tube opening increased linearly with the number of bystanders. The number of bystanders also increased the latency of the tutors' demonstration. Taken together, the results suggest that the spread of innovations within a population will be exponential, rather than sigmoidal as predicted by the contagion model: As the skill spreads, the rate of learning increases as a result of the dual effects of increased tutor number and reduced bystander number. © 1994 The Association for the Study of Animal Behaviour.