Abstract In many statistical solar flare studies, power laws are claimed and exponents derived by fitting a line to a log–log histogram. It is well known that this approach is statistically unstable, and very large statistics are needed to produce reliable exponent estimates. This may explain part of the observed divergence in power-law exponents in various studies. Moreover, the question is seldom addressed to what extent the data really do support power-law behavior. In this paper, we perform a comprehensive study of 6924 flares detected in SDO/AIA 9.4 nm images by the Solar Demon flare detection software between 2010 May 13 and 2018 March 16 and 9601 flares detected during the same period in GOES/XRS data by the LYRAFF flare detection software. We apply robust statistics to the SDO/AIA 9.4 nm peak intensity and the GOES/XRS raw peak flux, background-subtracted peak flux, and background-subtracted fluence and find clear indications that most background-corrected data are not well described by a power law and that all are better described by a lognormal distribution, while the raw GOES/XRS peak flux is best described by a power law. This may explain the success of power-law fits in flare studies using uncorrected data. The behavior of flare distributions has important implications for large-scale science questions such as coronal heating and the nature of solar flares. The apparent lognormal character of flare distributions in our data sets suggests that the assumed power-law nature of flares and its consequences need to be reexamined with great care.