The UN will formulate ambitious Sustainable Development Goals for 2030, including one for health. Feasible goals with some quantifiable, measurable targets can influence governments. We propose, as a quatitative health target, "Avoid in each country 40% of premature deaths (under-70 deaths that would be seen in the 2030 population at 2010 death rates), and improve health care at all ages". Targeting overall mortality and improved health care ignores no modifiable cause of death, nor any cause of disability that is treatable (or also causes many deaths). 40% fewer premature deaths would be important in all countries, but implies very different priorities in different populations. Reinforcing this target for overall mortality in each country are four global subtargets for 2030: avoid two-thirds of child and maternal deaths; two-thirds of tuberculosis, HIV, and malaria deaths; a third of premature deaths from non-communicable diseases (NCDs); and a third of those from other causes (other communicable diseases, undernutrition, and injuries). These challenging subtargets would halve under-50 deaths, avoid a third of the (mainly NCD) deaths at ages 50-69 years, and so avoid 40% of under-70 deaths. To help assess feasibility, we review mortality rates and trends in the 25 most populous countries, in four country income groupings, and worldwide.UN sources yielded overall 1970-2010 mortality trends. WHO sources yielded cause-specific 2000-10 trends, standardised to country-specific 2030 populations; decreases per decade of 42% or 18% would yield 20-year reductions of two-thirds or a third.Throughout the world, except in countries where the effects of HIV or political disturbances predominated, mortality decreased substantially from 1970-2010, particularly in childhood. From 2000-10, under-70 age-standardised mortality rates decreased 19% (with the low-income and lower-middle-income countries having the greatest absolute gains). The proportional decreases per decade (2000-10) were: 34% at ages 0-4 years; 17% at ages 5-49 years; 15% at ages 50-69 years; 30% for communicable, perinatal, maternal, or nutritional causes; 14% for NCDs; and 13% for injuries (accident, suicide, or homicide).Moderate acceleration of the 2000-10 proportional decreases in mortality could be feasible, achieving the targeted 2030 disease-specific reductions of two-thirds or a third. If achieved, these reductions avoid about 10 million of the 20 million deaths at ages 0-49 years that would be seen in 2030 at 2010 death rates, and about 17 million of the 41 million such deaths at ages 0-69 years. Such changes could be achievable by 2030, or soon afterwards, at least in areas free of war, other major effects of political disruption, or a major new epidemic.UK Medical Research Council, Norwegian Agency for Development Cooperation, Centre for Global Health Research, and Bill & Melinda Gates Foundation.