The motivation for our study is the disputed cause for the strong variation of 14 C around AD 775. Our method is to compare the 14 C variation around AD 775 with other periods of strong variability. Our results are: (a) We see three periods, where 14 C varied over 200 yr in a special way showing a certain pattern of strong secular variation: after a Grand Minimum with strongly increasing 14 C, there is a series of strong short-term drop(s), rise(s), and again drop(s) within 60 yr, ending up to 200 yr after the start of the Grand Minimum. These three periods include the strong rises around BC 671, AD 775, and AD 1795. (b) We show with several solar activity proxies (radioisotopes, sunspots, and aurorae) for the AD 770s and 1790s that such intense rapid 14 C increases can be explained by strong rapid decreases in solar activity and, hence, wind, so that the decrease in solar modulation potential leads to an increase in radioisotope production. (c) The strong rises around AD 775 and 1795 are due to three effects, (i) very strong activity in the previous cycles (i.e. very low 14 C level), (ii) the declining phase of a very strong Schwabe cycle, and (iii) a phase of very weak activity after the strong 14 C rise -very short and/or weak cycle(s) like the suddenly starting Dalton minimum. (d) Furthermore, we can show that the strong change at AD 1795 happened after a pair of two packages of four Schwabe cycles with certain hemispheric leadership (each package consists of two Gnevyshev-Ohl pairs, respectively two Hale-Babcock pairs). We show with several additional arguments that the rise around AD 775 was not that special. We conclude that such large, short-term rises in 14 C (around BC 671, AD 775, and 1795) do not need to be explained by highly unlikely solar super-flares nor other rare events, but by extra-solar cosmic rays modulated due to solar activity variations.