Geomagnetic models based on direct observations since the 1830s show that the averaged relative change in field intensity on Earth's surface over the past 170 years is less than 4.8% per decade. It is unknown if these rates represent the typical behavior of secular variations due to insufficient temporal resolution of archaeomagnetic records from earlier periods. To address this question, we investigate two ancient slag mounds in Cyprus-Skouriotissa Vouppes (SU1, fourth to fifth centuries CE, 21 m in height), and Mitsero Kokkinoyia (MK1, seventh to fifth centuries BCE, 8 m in height). The mounds are multilayered sequences of slag and charcoals that accumulated near ancient copper production sites. We modeled the age-height relation of the mounds using radiocarbon dates, and estimated paleointensities using Thellier-type IZZI experiments with additional anisotropy, cooling rate, and nonlinear TRM assessments. To screen out ambiguous paleointensity interpretations, we applied strict selection criteria at the specimen/sample levels. To ensure objectivity, consistency, and robust error estimation, we employed an automatic interpretation technique and put the data available in the MagIC database. The analyses yielded two independent subcentury-scale paleointensity time series. The MK1 data indicate relatively stable field at the time the mound accumulated. In contrast, the SU1 data demonstrate changes that are comparable in magnitude to the fastest changes inferred from geomagnetic models. We suggest that fast changes observed in the published archaeomagnetic data from the Levant are driven by two longitudinally paired regions, the Middle East and South Africa, that show unusual activity in geomagnetic models.