We examine a few cases in which subtle changes in how an external forcing is applied lead to climate responses that are qualitatively opposite to each other.  First, we consider the case of an idealized thermal forcing centered at the equator in the troposphere.  We show that the circulation response is highly sensitive to the meridional extent of the thermal forcing, and we construct a simple diffusive model that explains this sensitivity.  Next, we consider the case of solar forcing in an atmospheric GCM coupled to a mixed-layer ocean.  We show that the response to a small increase in total solar irradiance depends greatly on the background state that the forcing is applied to.  Specifically, a forcing applied to a present-day climate produces a response that is very different from a forcing applied to a doubled-CO2 climate. These sensitivities are very much relevant to understanding climate change and variability on decadal to centennial timescales.