Leibniz' first problem with contingency stems from his doctrine of divine creation (not his later doctrine of truth) and is solved via his concepts of necessity per se, etc. (not via his later concept of infinite analysis). I scrutinize some of the earliest texts in which the first problem and its solution occur. I compare his "per se modal concepts" with his concept of analysis and with the traditional concept of metaphysical necessity. I then identify and remove the main obstacle to Leibniz' employment of these concepts by reflecting on his concept of a world and comparing and contrasting it with contemporary conceptions. Finally I sketch the place that this early problem and its solution had in the context of his mature philosophy. A disagreement between Sleigh and Adams which hinges on the assumption that there is just one problem with competing solutions is seen to dissolve in this light.