In the context of flow-aware networking, size-based (SB) scheduling policies have been shown to improve response times of small flows, without degrading the performance of large flows. But these differentiating policies are designed for Output-queued (OQ) switch architecture, which is known to have scalability issues. On the other hand, the buffered-crossbar (BX) switch architecture is currently being pursued as a potential next-generation scalable switch architecture. This work looks into the problem of performing SB scheduling in BX switches. In particular, the design goals, with respect to each output port, are (i) to transmit high-priority packet(s) as long as there is at least one present, and (ii) to respect the FIFO order among high-priority packets. In this direction, we propose a CICQ switches using a single PIFO queue at each crosspoint to schedule packets according to the priority assigned. pCICQ-1 switch uses a simple design to guarantee that packet-priorities are respected once they are in the crosspoint queues. But it does not maintain the FIFO order of high-priority packets, besides letting a bounded number low-priority packets to depart through an output, when there are one or more high-priority packets for the same output. To solve this, we propose an enhancement in pCICQ-2 switch, that uses a sequence controller to respect packet-priorities as well as arrival order for high-priority packets.