A packet processor of a network device determines an amount of free buffer space in a buffer memory currently available for buffering packets, and dynamically determines a value of a threshold for triggering a particular traffic management operation with respect to a packet, to dynamically adjust the value of the threshold based at least in part on a changing amount of free buffer space available for buffering packets in the buffer memory. The packet processor determines, based on a comparison between i) a current fill level of a particular transmit queue in which the packet is to be enqueued and ii) the dynamically adjusted value of the threshold, whether the particular traffic management operation is to be triggered with respect to the packet. When the particular traffic management operation is to be triggered, the packet processor performs the particular traffic management operation with respect to the packet.