Over the last decade, the field of radiocarbon analysis has been revolutionized by the discovery of single-year anomalies, because they can be used as markers of space weather events and as time anchors for exact dating. Brehm et al. (2021) recently analyzed two new anomalies, in the years 1052 CE and 1279 CE. These candidates show consecutive year Δ14C increases of 5.9‰ and 6.5‰, respectively. In this study, we measured and analyzed dendrochronologically dated oak wood samples from northern Europe spanning both these years. Our results, although statistically consistent with those presented in the original publication, show effectively no increase in Δ14C (1 and 2.5 times the measurement error, respectively). Nonetheless, we proceed to analyze our datasets with the aid of the open-source Python package ticktack. Our modeled outputs confirm that radiocarbon production barely rose above background levels across these two periods, and no event of clearly resolvable start date or duration could be detected. Additionally, we conduct the same analyses on a new sample spanning the years 531–550 CE. Here, once again, only weak evidence was obtained for any increase in radiocarbon production, and no significant annual rise was evident. The gradual increases exhibited by all three of these samples, and the ubiquity of these patterns across the calibration curve, call into question any likely cosmic event in these cases, and illustrate how challenging it will be to distinguish lower magnitude events in the radiocarbon record.