How the solar electromagnetic energy entering the Earth's atmosphere varied since preindustrial times is an important consideration in the climate change debate. Detrimental to this debate, estimates of the change in total solar irradiance (TSI) since the Maunder minimum, an extended period of weak solar activity preceding the industrial revolution, differ markedly, ranging from a drop of 0.75 W m −2 to a rise of 6.3 W m −2. Consequently, the exact contribution by solar forcing to the rise in global temperatures over the past centuries remains inconclusive. Adopting a novel approach based on state-of-the-art solar imagery and numerical simulations, we establish the TSI level of the Sun when it is in its least-active state to be 2.0 ± 0.7 W m −2 below the 2019 level. This means TSI could not have risen since the Maunder minimum by more than this amount, thus restricting the possible role of solar forcing in global warming. Plain Language Summary How the amount of energy the Earth receives from the Sun varied since preindustrial times is an important consideration in the climate change debate. Detrimental to this debate, it is not known whether the Sun grew brighter or dimmer since the 16th century, and by how much. As a consequence, the exact contribution by fluctuations in the brightness of the Sun to the rise in global temperatures over the past centuries remains controversial. It is established that the Sun was particularly inactive over much of the 16th century. Adopting a novel approach based on state-of-the-art solar imagery and computer models, we determined the brightness of the Sun when it is in its least-active state possible. This places a strict limit on how much the Sun could have grown brighter since the lull in solar activity over the 16th century, restricting the possible role the Sun could have played in global warming. Since the reliable measurement of solar irradiance only started in 1978 (Kopp, 2014), climate simulations rely on models of solar irradiance variability to provide the requisite historical solar forcing input. Except at RESEARCH LETTER