A description is given of the structure and precipitation sequence of AlCu4.5 alloys with a magnesium content between those of binary AlCu and quasi-binary AlCuMg alloys. For alloys with a small magnesium content (0.23 wt%) these are the coherent copper-like Guinier-Preston zones and the incoherent Theta’ and Theta phases with an adequate content of dissolved magnesium, so the precipitation sequence can be essentially realized without any difficulty. In the case of higher magnesium concentration, a re-orientation occurs because it requires both time and energy. An undisturbed transition to the Theta(Mg) phase is impossible. The phase structure becomes more similar to that of the S phase but it is unsafe to describe it as a quasi-binary structure. The different sizes which develop between the AlCu4.5 and AlCuMg0.98 alloys are discussed.