Thinner Si solar cells with higher efficiency can make a Si photovoltaic system a cost-effective energy solution, and nanostructuring has been suggested as a promising method to make thin Si an effective absorber. However, thin Si solar cells with nanostructures are not efficient because of severe Auger recombination and increased surface area, normally yielding <50% EQE with short-wavelength light. Here we demonstrate >80% EQEs at wavelengths from 400 to 800 nm in a sub-10-μm-thick Si solar cell, resulting in 13.7% power conversion efficiency. This significant improvement was achieved with an all-back-contact design preventing Auger recombination and with a nanocone structure having less surface area than any other nanostructures for solar cells. The device design principles presented here balance the photonic and electronic effects together and are an important step to realizing highly efficient, thin Si and other types of thin solar cells.