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The Value of Information (VoI) assesses the impact of data in a decision process. A risk-neutral agent, quantifying the VoI in monetary terms, prefers to collect data only if their VoI surpasses the cost to collect them. For an agent acting without external constraints, data have non-negative VoI (as free “information cannot hurt”) and those with an almost-negligible potential effect on the agent's belief have an almost-negligible VoI. However, these intuitive properties do not hold true for an agent acting under external constraints related to epistemic quantities, such as those posed by some regulations. For example, a manager forced to repair an asset when its probability of failure is too high can prefer to avoid collecting free information about the actual condition of the asset, and even to pay in order to avoid this, or she can assign a high VoI to almost-irrelevant data. Hence, by enforcing epistemic constraints in the regulations, the policy-maker can induce a range of counter-intuitive, but rational, behaviors, from information avoidance to over-evaluation of barely relevant information, in the agents obeying the regulations. This paper illustrates how the structural properties of VoI change depending on such external epistemic constraints, and discusses how incentives and penalties can alleviate these induced attitudes toward information.