The Distributed Constraint Optimization Problem (DCOP) formulation is a powerful tool to model cooperative multi-agent problems, especially when they are sparsely constrained with one another. A key assumption in this model is that all constraints are fully specified or known a priori, which may not hold in applications where constraints encode preferences of human users. In this paper, we extend the model to Incomplete DCOPs (I-DCOPs), where some constraints can be partially specified. User preferences for these partially-specified constraints can be elicited during the execution of I-DCOP algorithms, but they incur some elicitation costs. Additionally, we extend SyncBB, a complete DCOP algorithm, and ALS-MGM, an incomplete DCOP algorithm, to solve I-DCOPs. We also propose parameterized heuristics that those algorithms can utilize to trade off solution quality for faster runtime and fewer elicitation. They also provide theoretical quality guarantees when used by SyncBB when elicitations are free. Our model and heuristics thus extend the state-of-the-art in distributed constraint reasoning to better model and solve distributed agent-based applications with user preferences.