The simple and cheap memory-less RFID tag systems have found many diverse applications. The available singulation algorithms for such systems adopt either single-slot or multi-slot frames with a fixed frame size, independent of tag population. A single-slot scheme has good performance in terms of the number of overall slots N, but it can cause a very large number of requests R. A multi-slot scheme, on the other hand, achieves good performance of R, but it may introduce an unacceptable large N. In this paper, we propose an adaptive frame size singulation scheme for memory-less RFID systems. Our basic idea is to adaptively choose a suitable frame size based on tag population information collected during the singulation, such that the number of unnecessary collision and idle slots can be reduced. Analytical models are also derived for the performance analysis of the new scheme. Surprisingly, our theoretical and simulation studies indicated that through adopting such adaptive frame size, the new singulation scheme can achieve a performance of N as good as the single-slot scheme, and at same time, guarantees a performance of R similar to the available multi-slot schemes.