The openness of decision-makers to be influenced by and invest in proposals for policy reform is not constant. Timing is key, as are the diversity and depth of interests, levels of knowledge, and nature of the policy challenge itself; these can all affect how governments absorb information that might fall beyond the usual cost-benefit assessments of day-to-day policymaking. This essay explores how and when the policy environment provides opportunities to introduce a more nuanced discussion of competing moral values in migration governance and, critically, the new policy directions to which they might give rise. In doing so, it will utilize a range of examples from national, EU, and global debates of the past decade, to highlight moments when a dilemmas approach has been—or could have been—useful to effect policy change. Stressing ethical dilemmas can influence migration policymakers when the conditions are right.