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Despite unprecedented progress towards lower under-five mortality in high-mortality countries in recent years, a large fraction of these countries will not attain the numerical target under Millennium Development Goal (MDG) 4, a reduction of the mortality rate by two-thirds compared to levels in 1990. Nevertheless, many stakeholders have argued that the post-2015 agenda should contain a level-end goal for under-five mortality and recent accelerations in the rate of reduction in under-five mortality have been cited as a cause for optimism. We argue in this paper that one key fact about relative changes in mortality rates is a lack of persistence. We find robust evidence for substantial mean reversion in the data. Hence, recent accelerations observed for countries in Sub-Saharan Africa are an overly optimistic estimate of future reductions. At the same time, progress as required by the old MDG4 coincides very much with our projections for Sub-Saharan Africa and other regions. Thus, while MDG4 has been rightly criticized as overly ambitious and unfair to Africa for the 1990-2015 period, such a goal seems more appropriate for the 2005-2030 period. We also offer a discussion of likely drivers of future reductions in child deaths.