The new IntCal20 radiocarbon record continues decades of successful practice by employing one calibration curve as an approximation for different regions across the hemisphere. Here we investigate three radiocarbon time-series of archaeological and historical importance from the Mediterranean-Anatolian region, which indicate, or may include, offsets from IntCal20 (~0-22 14C years). While modest, these differences are critical for our precise understanding of historical and environmental events across the Mediterranean Basin and Near East. Offsets towards older radiocarbon ages in Mediterranean-Anatolian wood can be explained by a divergence between high-resolution radiocarbon dates from the recent generation of accelerator mass spectrometry (AMS) versus dates from previous technologies, such as low-level gas proportional counting (LLGPC) and liquid scintillation spectrometry (LSS). However, another reason is likely differing growing season lengths and timings, which would affect the seasonal cycle of atmospheric radiocarbon concentrations recorded in different geographic zones. Understanding and correcting these offsets is key to the well-defined calendar placement of a Middle Bronze Age tree-ring chronology. This in turn resolves long-standing debate over Mesopotamian chronology in the earlier second millennium BCE. Last but not least, accurate dating is needed for any further assessment of the societal and environmental impact of the Thera/Santorini volcanic eruption.