To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference algorithms operate over the network to answer queries. Recognizing the inflexibility of fixed models has led researchers to develop automated network construction procedures that use an expressive knowledge base to generate a network that can answer a query. Although more flexible than fixed model approaches, these construction procedures separate construction and evaluation into distinct phases. In this paper we develop an approach to combining incremental construction and evaluation of a partial probability model. The combined method holds promise for improved methods for control of model construction based on a trade-off between fidelity of results and cost of construction.