Recent reconstructions of total solar irradiance (TSI) postulate that quiet-Sun variations could give significant changes to the solar power input to Earth's climate (radiative climate forcings of 0.7–1.1 W m−2 over 1700–2019) arising from changes in quiet-Sun magnetic fields that have not, as yet, been observed. Reconstructions without such changes yield solar forcings that are smaller by a factor of more than 10. We study the quiet-Sun TSI since 1995 for three reasons: (i) this interval shows rapid decay in average solar activity following the grand solar maximum in 1985 (such that activity in 2019 was broadly equivalent to that in 1900); (ii) there is improved consensus between TSI observations; and (iii) it contains the first modelling of TSI that is independent of the observations. Our analysis shows that the most likely upward drift in quiet-Sun radiative forcing since 1700 is between +0.07 and −0.13 W m−2. Hence, we cannot yet discriminate between the quiet-Sun TSI being enhanced or reduced during the Maunder and Dalton sunspot minima, although there is a growing consensus from the combinations of models and observations that it was slightly enhanced. We present reconstructions that add quiet-Sun TSI and its uncertainty to models that reconstruct the effects of sunspots and faculae.@en