Short-term fluctuations in atmospheric radiocarbon (14C) concentration mark the tree-ring record for the last ∼15 kyr. Terrestrial macrofossils from sediment cores of Lake Suigetsu, Japan, extend this record of fluctuations back to >35 cal ka BP. Their significance, however, is under debate since the signal-to-noise ratio of the Suigetsu record is low and progressively decreases with increasing age. Coherent semi-millennial-scale structures of the Suigetsu 14C record have nevertheless been identified by three different techniques, namely visual inspection, analyses of the first derivative of 14C vs. calendar age, and Bayesian spline inflections of 14C concentration vs. calendar age, and hence appear objectively real. These 14C fluctuations correlate closely with those of the tree-ring-based 14C master record ∼10–14 cal ka. Thus, Suigetsu fine structures attain global significance and may properly reflect atmospheric 14C variability back to ∼35 cal ka. Carbonate-based 14C records from speleothems and ocean sediments are far smoother and form, together with Suigetsu and other data, the backbone of the IntCal20 record >14 cal ka that largely lacks the Suigetsu fine structure. 14C decay reduces 14C-signal amplitudes over time, so Holocene-style 14C signals of solar modulation disappear in the noise beyond ∼10 cal ka. The remaining older 14C fine structures had larger forcings, most likely linked to climate and carbon cycle, especially ocean-atmosphere CO2 exchange, and thus contain valuable information about these factors. They may also provide global stratigraphic tie points to correlate 14C records of oceanic plankton sediments and climate signals independent of problems with local 14C reservoir effects.