Measurements [3,4,5] have shown that the rate of growth of routes and route instances in the default-free table have resumed exponential growth, which had slowed to linear growth after the introduction of CIDR [7]. This memorandum explores some analytical methods, admittedly heuristic in most cases, to understand why growth is faster than the simple rate of allocation. When accelerated growth can be attributed to operational practices or poor understanding, it may be possible to propose approaches to reducing the rate of table explosion without reducing the services delivered to end users.