The design of optical buffers for packet contention resolution has been recognized as a key issue in all-optical packet switching. One of the most general buffering schemes is priority queues, which includes first-in first-out (FIFO) queues and last-in first-out (LIFO) queues as special cases. In a priority queue, each packet is associated with a unique priority upon its arrival, the packet with thehighestpriority is sent out from the queue whenever there is a departure request and there are packets in the queue, and the packet with thelowestpriority is dumped from the queue whenever there is a buffer overflow. In this paper, we consider the constructions of optical priority queues by using a feedback system consisting of an optical (bufferless) crossbar switch and multiple optical FIFO multiplexers with delay one (FM1’s) in the feedback path for buffering packets and feeding packets back to the switch. Such a feedback system is a generalization of that used in one of the authors’ earlier attempt for the constructions of optical priority queues in Tanget al.(2020). We fix theno-bufferingproblem in Tanget al.(2020) by using optical FM1’s to replace the optical FIFO multiplexers (FM’s) in Tanget al.(2020), which enables us to successfully achieve an exact emulation of a priority queue. We improve the utilization of buffering capacity over that in Tanget al.(2020) by routing packets to the optical FM1’s according to theirbuffering tagsinstead of theirtagsas used in Tanget al.(2020). We also extend and generalize the construction in Tanget al.(2020) and obtain a much larger class of constructions of optical priority queues. Our constructions are made possible by showing that the highest-priority (resp., lowest-priority) packet is always available at the input links of the switch whenever it needs to be routed to the departure (resp., loss) link, and by showing that there is no collision and there is no buffer overflow at any FM1 at any time so that there is no internal packet loss at any time. Our complexity analysis shows that by using a feedback system consisting of an optical$(M+2) \times (M+2)$(bufferless) crossbar switch and$M$fiber delay lines, we can achieve a buffer size of$2^{O(\sqrt {\alpha M})}$, where$\alpha $is a constant that depends on the parameters used in our constructions. Furthermore, we show that the best buffer size that we can achieve is$2^{O(\sqrt {4M/15})}$. Our result (exponential in$\sqrt {M}$) substantially improves on the best known result (polynomial in$M$) in the literature. Our numerical results show that the construction complexity of our constructions is lower than that of the construction in Tanget al.(2020), and the actual saving, in terms of the number of$2\times 2$switches needed, by our constructions could be quite significant even in the tiny-buffer and small-buffer regimes.