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The proper offensive against uncertainty in these circumstances is the pursuit of what we call "early wins." These are nuggets of reassurance which send positive signals to all stakeholders and all observers. They reflect substantial and sustainable results. When properly achieved and positively communicated, they serve to create, maintain and expand a store of goodwill. This in turn helps you obtain buy-in and generate the motivation which keeps the merged company moving forward toward the longer-term goals which some may still have a hard time grasping or visualizing.
This may sound like another simple and obvious "common sense" rule. Who can argue with the recommendation that newly-merged companies should strive to achieve early wins to obtain buy-in from the organization?