When children first learn to count, what do they understand about the structure of the count system? The present study investigated English-speaking children's ability to generalize the rules that structure their count list to novel contexts. A total of N = 86 children (3;0-6;11) completed a battery of tasks aimed at measuring their understanding of the English count list: they counted as high as they could, and were asked to generate successors to English numbers (e.g., "Fifty-seven: what comes next?"). Next, they were introduced to novel decade terms, and were asked to generate successors to numbers containing those terms (e.g., "Blicky-seven: what comes next?"). Children's ability to generate successors was predicted by their counting ability, and a sizeable subset of children were able to generate successors both for novel numbers and for English numbers outside their productive count range. These data suggest that emerging counters can use their understanding of the structure of the English count list to generate successors to unfamiliar numbers.