In general, with the addition of solutes, the yield strength of alloys is expected to increase; this phenomenon is known as solid solution strengthening. However, this model of strengthening implicitly assumes that dislocations are available and it is their motion that causes plastic deformation. On the other hand, in dislocation starved regimes, it is the nucleation of dislocations that controls the deformation behaviour. In this regime, the solute atoms can act as sites of heterogeneous nucleation for dislocations and “anomalous” softening with alloying additions are not uncommon. In this study, using Molecular Dynamics (MD) simulations, we show anomalous softening in Cu–Al alloys deformed at 300 K. We show that there are two components to this softening; in addition to the heterogeneous nucleation at solute sites, the reduction in stacking fault energy with alloying addition promotes the (homogeneous) nucleation of partial dislocation loops. In order to be consistent, we interpret the MD simulation results of deformation behaviour using parameters and energies derived from the same potentials used in the simulations. Specifically, we carry out the thermodynamic integration to evaluate the free energies in crystals with and without the stacking faults and hence calculate the SFE as a function of Al content at 300 K. Using the SFE values thus obtained, and using a continuum model of homogeneous nucleation of partial dislocation loops, we rationalise the deformation behaviour seen in pure copper. On the other hand, in Cu–Al alloys, the drop in yield strength can only be explained using a combination of the continuum model (which assumes homogeneous nucleation), and the reduction in heterogeneous nucleation barrier (which is a function of the ratio of the unstable and stable stacking fault energies). Thus, our results indicate that deformation experiments of pure copper and copper–aluminium alloys in the dislocation starved regime could be interesting and might show qualitatively and quantitatively different behaviour.