Laser ablation (LA) accelerator mass spectrometry (AMS) is a novel method for rapid online radiocarbon (14C) analysis of carbonates. The quasi-continuous 14C profiles obtained with this technique demand a customized data evaluation protocol to relate the acquired 14C data to the analyzed sample. We take into account the mixing effects due to the minimal counting (integration) time of the AMS, the finite width of the laser beam and the gas washout of the ablation volume. Thereby we mathematically describe our LA setup with a system function that acts on the produced CO/CO2 (COX) from the sample resulting in a mixing of the 14C profiles obtained by AMS analysis. Furthermore, we analyze the long-term target memory effect in the gas ion source and establish a routine for correction. The correction routine is tested with a stalagmite comprising a growth stop that is analyzed at different scanning velocities indicating that only the slow scanning velocity can provide the necessary resolution to determine the width of the growth stop of 365 μm.