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Distributed Constraint Optimization Problems (DCOPs) is a framework for representing and solving distributed combinatorial problems, where agents exchange messages to assign variables they own, such that the sum of constraint costs is minimized. When agents represent people (e.g., in meeting scheduling problems), the constraint information that the agents hold may be incomplete. For such scenarios, researchers proposed Incomplete DCOPs (I-DCOPs), which allow agents to elicit from their human users some of the missing information. Existing I-DCOP approaches evaluate solutions not only by their quality, but also the elicitation costs spent to find them (ex-post). Unfortunately, this may result in the agents spending a lot of effort (in terms of elicitation costs) to find high-quality solutions, and then ignoring them because previous lower-quality solutions were found with less effort. Therefore, we propose a different approach for solving I-DCOPs by evaluating solutions based on their quality and considering the elicitation cost beforehand (ex-ante). Agents are limited in the amount of information that they can elicit and, therefore, need to make smart decisions on choosing which missing information to elicit. We propose several heuristics for making these decisions. Our results indicate that some of the heuristics designed produce high-quality solutions, which significantly outperform the previously proposed ex-post heuristics.