The fast dynamic measurement of connection bandwidth utilizes a single pair of packets to calculate bandwidth between two entities on a network (such as the Internet). This calculation is based upon the packet-pair technique. This bandwidth measurement is extremely quick. On its journey across a network, communication equipment and modems may compress a packet. This compression shrinks the size of the packet; thus, it can distort the bandwidth calculation using such a shrunken packet. To avoid this distortion, the fast dynamic measurement of connection bandwidth employs non-compressible packets. More specifically, it employs highly entropic packets. Therefore, a packet cannot be compressed during its journey. In addition, on its journey across a network, packets may be rerouted, delayed, misrouted, and the like. These momentary delays may result in a momentary bad bandwidth calculation. This problem is ameliorated by using a history list at the client that keeps track of recent measurements. The client returns the median of that list to the server. That median is the specified bandwidth.