The Single Ion Differential α Measurement (SIDAM)method for measuring Δα/α and its figures of merit are illustrated together withthe results produced by means of Fe ii absorption linesof QSO intervening systems. The method providesΔα/α = -0.12 ±1.79 ppm (parts-per-million) at zabs = 1.15towards HE 0515-4414 and Δα/α = 5.66±2.67 ppm at zabs = 1.84towards Q 1101-264, which are so far the most accurate measurementsfor single systems. SIDAM analysis for 3 systems from the Chand et al. [1]sample provides inconsistent results which we interpret as due tocalibration errors of the Chand et al. data at the level ≈10 ppm.In one system evidence for photo-ionization Dopplershift between Mg ii and Fe ii lines is found.This evidence has important bearings on the Many Multipletmethod where the signal for Δα/αvariabilityis carried mainly by systems involving Mg ii absorbers.Some correlations are also found in the Murphy et al. [10] sample which suggestlarger errors than previously reported.Thus, we consider unlikely that both the Chand et al.and Murphy et al. datasets could providean estimate of Δα/α with an accuracy at the level of 1 ppm.A new spectrograph like the ESPRESSO projectwill be crucial to make progress in the astronomical determination of Δα/α.