In our previous study [Phys. Rev. B 86, 201104 (2012).] we introduced the so-called quasi-non-uniform gradient-level exchange-correlation approximation (QNA) and demonstrated its strength in producing highly accurate equilibrium volumes for metals and their alloys within density-functional theory. In this paper we extend the scheme to include the accuracy of the bulk modulus as an additional figure of merit and show that this scheme is flexible enough to allow the computation of accurate equilibrium volumes and bulk moduli at the same time. The power and feasibility of this scheme is demonstrated on NiAl and FeV binary alloys.