Fuzzy constraints are a popular approach to handle preferences and over-constrained problems. We consider here situations where some of the preferences may be missing. This models, for example, settings where agents are distributed, or have privacy issues, or where there is an ongoing preference elicitation process. We study how to find a solution which is optimal irrespective of the missing preferences, eliciting preferences from the user if necessary. Our goal is to ask the user as little as possible. To solve this task, we define a combined solving and preference elicitation scheme with a large number of different instantiations which we test on randomly generated problems. Our experimental results show that some of the algorithms are very good at finding a necessarily optimal solution while asking only a very small fraction of the missing preferences to the user. We also test the algorithms on hard constraint problems with possibly missing constraints. The aim now is to find feasible solutions irrespective of the missing constraints.