HR-CS-GFAAS methods were developed for the fast determination of Cu in domestic and commercially available Hungarian distilled alcoholic beverages (called pálinka), in order to decide if their Cu content exceeds the permissible limit, as legislated by the WHO. Some microliters of samples were directly dispensed into the atomizer. Graphite furnace heating programs, effects/amounts of the Pd modifier, alternative wavelengths (e.g., Cu I 249.2146 nm), external calibration and internal standardization methods were studied. Applying a fast graphite furnace heating program without any chemical modifier, the Cu content of a sample could be quantitated within 1.5 min. The detection limit of the method is 0.03 mg/L. Calibration curves are linear up to 10–15 mg/L Cu. Spike-recoveries ranged from 89% to 119% with an average of 100.9 ± 8.5%. Internal calibration could be applied with the assistance of Cr, Fe, and/or Rh standards. The accuracy of the GFAAS results was verified by TXRF analyses.