1. Several probability models are used to examine the hypothesis that mud-nesting Hymenoptera include empty, yet sealed, cells in their nests to reduce the success of parasites that break into the nest after its completion and destroy the immature host therein. We examine optimal empty cell placement when parasites choose cells randomly and abandon a host nest after encountering one or two consecutive empty cells. We also consider cases in which parasites begin hunting (1) randomly, or (2) peripherally and then proceed unidirectionally until either all nest cells have been parasitized or two consecutive empty cells have been encountered. 2. In all cases the host may increase net reproductive output by appropriate placement of empty cells. Parasites may combat empty cell placement by hosts by evolving a persistent, random search hunting method. 3. The literature on empty cell inclusion in mud nests is examined, and one tentative case, that of Pseudomasaris vespoides (Cress.), is discussed.