Results of a Doppler broadening positron annihilation study on crystalline, quasicrystalline and amorphous Al-Cu-T (T=FeV) alloys are presented. For the first time it is shown that a quasicrystal (Al₆₅Cu₂₀Fe₁₅) can be prepared with a positron trapping site concentration below the sensitivity of positron annihilation spectroscopy. The results and those of similar studies previously reported for quasicrystalline Al-Mn-Si and Al-Cu-Li are discussed in conjunction with possible stabilisation mechanisms.