Nowadays, most radiocarbon (14C) laboratories can reliably avoid and remove any possible sample contamination during the pretreatment of organic samples (e.g., bones, charcoal, or trees) thanks to a series of methods commonly used by the radiocarbon community. However, what about the final step, the storage of graphite? Rarely do the laboratories produce their graphite and ship it as pressed targets to accelerator mass spectrometry (AMS) facilities for measurement. Pressed graphite in aluminum targets are vulnerable to contamination, and during shipment or storage, exogenous carbon can be introduced again. Here we report a test on various archaeological sample materials from different environments and different periods (from the past three millennia to the Middle Paleolithic period). We transformed them into graphite, pressed the graphite into targets and sent them to two different AMS laboratories to be dated. We observe that packing details of the targets, extended shipment and storage time may lead to contamination which can be avoided by appropriate packaging in tight metal cans and sealed in vacuum bags. Close cooperation and coordination between our chemistry laboratory and the AMS facilities, high standards in contamination removal, and efficient measurement planning enabled us to obtain reliable 14C ages within a short time.