We perform numerical simulations of the atmosphere, sea ice and upper ocean to examine possible effects of diminishing incoming solar radiation, insolation, on the climate system. We simulate both global and Arctic climate engineering in idealized scenarios in which insolation is diminished above the top of the atmosphere. We consider the Arctic scenarios because climate change is manifesting most strongly there. Our results indicate that, while such simple insolation modulation is unlikely to perfectly reverse the effects of greenhouse gas warming, over a broad range of measures considering both temperature and water, an engineered high CO2 climate can be made much more similar to the low CO2 climate than would be a high CO2 climate in the absence of such engineering. At high latitudes, there is less sunlight deflected per unit albedo change but climate system feedbacks operate more powerfully there. These two effects largely cancel each other, making the global mean temperature response per unit top-of-atmosphere albedo change relatively insensitive to latitude. Implementing insolation modulation appears to be feasible.