Abstract High-income countries (HICs), including UK, Germany and Japan, are reducing CO2 output relative to economic growth. SDG8 refers to 'sustainable growth' but does not differentiate between low, middle- and high-income countries. The United Nations target is for net-zero CO2 emissions by 2050, therefore there is a strong case for exploring the implications of low or zero economic growth among HICs as a mechanism for limiting climate change. A key consideration is whether progress in population health would stall if HIC economies stopped growing. We examined headline health statistics among HIC countries for evidence of divergence in health trends. We looked for associations between trajectories of national economies and health trends over the past four decades. Age-standardised death rates were calculated from all-cause and cause-specific rates in the WHO mortality database. All-cause mortality (ACM) rates declined in parallel in UK, France and Japan, from about 700 to 400/100,000 in the period 1980-2010, with the lowest rates in Japan. Decline in the ACM rate in USA was shallower 1980-2010. In the decade of austerity following the banking crisis, the ACM rate in USA and UK stopped declining. The Japanese ACM rate continued its rapid post-war decline in the two decades of economic stagnation after 1990. Trends in Japanese coronary heart disease, stroke and cancer mortality rates, but not those for suicide, were consistently favourable in the recent period. The natural before-and-after experiment in Japan, of high economic growth in the decades to 1990, and low growth after 1990, is an example of a HIC with continuing progress in population health in a long period of low growth. Repeat measures of subjective, self-rated health from a population-based Japanese survey series (1986-2013) add to the evidence from objective mortality rate trends. Progress in population health does not need to stall if HIC economies focus on combatting climate change instead of growth.