This paper investigates methods that balance time and space constraints against the quality of Bayesian network inferences - we explore the three-dimensional spectrum of "time×space×quality" trade-offs. The main result of our investigation is the adaptive conditioning algorithm, an inference algorithm that works by dividing a Bayesian network into sub-networks and processing each sub-network with a combination of exact and anytime strategies. The algorithm seeks a balanced synthesis of probabilistic techniques for bounded systems. Adaptive conditioning can produce inferences in situations that defy existing algorithms, and is particularly suited as a component of bounded agents and embedded devices. © 2004 Elsevier Inc. All rights reserved.