Lack of control on the chirality or diameter of single-wall carbon nanotubes (SWCNTs) during synthesis is a major impediment in the path of their widespread commercialization. We demonstrate that the humble technique of catalytic chemical vapor deposition of methane, without any sophisticated catalyst preparation, can provide significant control on the diameter of the synthesized SWCNTs. The catalyst used is a solid solution of the bimetals Fe-Mo or Co-Mo in MgO. The radial breathing modes (RBMs) in the Raman spectra of SWCNTs were used to find out the diameters. Kataura plot along with RBMs was used to study the chirality of the tubes. High concentration of the catalysts (Co:Mo:MgO = 1:0.5:15 and Fe:Mo:MgO = 1:0.5:30) resulted in high yields. However, most of these carbonaceous materials were impurities. Reducing the concentration not only improved the purity and crystallinity (ID/IG ratio ∼0.1), but most importantly reduced the diameter spread of the SWCNTs. Majority of the SWCNTs grown using the low concentration catalysts (Co:Mo:MgO = 1:0.5:300 and Fe:Mo:MgO = 1:0.5:200) were estimated to have diameters lying between 1.13 and 1.65 nm. This narrowing of diameter spread happened for both Fe and Co catalyst systems and depended only on the concentration of the catalyst.