Recombinative generalization is the production of responses in the presence of novel combinations of known components. For example, after learning "red triangle" and "blue square," recombinative generalization is observed when a child can tact "red square" and "blue triangle." Recombinative generalization can emerge from a history of matrix training, which involves carefully selecting and arranging stimuli and responses along at least two axes and training a subset of responses. With three children with autism spectrum disorder, we compared recombinative generalization of object-action or feature-object tacts when the component stimuli were trained before combination stimuli, trained along with combination stimuli, or untrained (i.e., combination only). For two participants, training the components along with some combinations led to the most untrained targets acquired without direct teaching. For the other participant, training the combinations only led to the greatest proportion of untrained targets acquired without direct teaching. We discuss stimulus control promoted by each teaching arrangement and suggestions for future research on recombinative generalization.