Estimates of climate sensitivity are typically characterized by highly asymmetric probability density functions (pdfs). The reasons are well known, but the situation leaves open an uncomfortably large possibility that climate sensitivity might exceed 4.5°C. In the contexts of (1) global-mean observations of the Earth's energy budget and (2) a global-mean feedback analysis, we explore what changes in the pdfs of the observations or feedbacks used to estimate climate sensitivity would be needed to remove the asymmetry, or to substantially reduce it, and demonstrate that such changes would be implausibly large. The nonlinearity of climate feedbacks is calculated from a range of studies and is shown also to have very little impact on the asymmetry. The intrinsic relationship between uncertainties in the observed climate forcing and the climate's radiative response to that forcing (i.e., the feedbacks) is emphasized. We also demonstrate that because the pdf of climate forcing is approximately symmetric, there is a strong expectation that the pdf of climate feedbacks should be symmetric as well.