Reasons for quantifying pottery, and the various measures of quantity that are available are reviewed, leading to a statement of the criteria that such measures should satisfy. Two new models for the breakage and retrieval of pottery -- Kirby processes and recursive sampling -- are presented and fitted to large groups of post-medieval pottery from a site at Aldgate, City of London. These models are used to assess the performance of four measures of quantity-sherd count, weight, vessels represented and vessel-equivalents -- under a wide variety of conditions, using computer simulation. Initial results show that only vessel-equivalents is unbiased under a range of conditions, but suggest that vessels represented may often give the lowest sampling error. The simulations are also used to suggest the minimum size of sample that can give reliable results, again under a range of conditions. See also AATA 16-752 and 21-189. -- AATA