The study presents several cases where use of specimens with reduced overall dimensions, i.e. mini specimens in the course of fatigue tests is advantageous. The high-cycle fatigue tests based on a developed method have been performed on mini specimens and normative specimens (comparative tests). The tests have been conducted on EN AW-6063 aluminum alloy specimens. A correction coefficient determined as a result of monotonic tests and selected models of the size effect have been critically assessed based on the test results. A statistical Weibull's weakest link model and a monofractal approach based on a fractal dimension have been verified.