We analyze a situation where an uninformed decision-maker has to decide on an issue. There are two parties with state-independent opposing interests who can acquire information in support of their cause through costly search. Information can be obtained across multiple dimensions. A decision is more complex the more dimensions are available for investigation. Each party has to decide on the number of searches it performs. If there is an asymmetry between the parties with regard to the utility they derive from decisions in their favor, we show that a reduction of complexity can lead to an overall increased and more balanced search which may improve welfare.