Cyclin‐dependent kinases (CDKs) 7 and 9 are deregulated in various types of human cancer and are thus viewed as therapeutic targets. Accordingly, small‐molecule inhibitors of both CDKs are highly sought‐after. Capitalising on our previous discovery of CDKI‐73, a potent CDK9 inhibitor, medicinal chemistry optimisation was pursued. A number of N‐pyridinylpyrimidin‐2‐amines were rationally designed, chemically synthesised and biologically assessed. Among them, N‐(6‐(4‐cyclopentylpiperazin‐1‐yl)pyridin‐3‐yl)‐4‐(imidazo[1,2‐a]pyrimidin‐3‐yl)pyrimidin‐2‐amine was found to be one of the most potent inhibitors of CDKs 7 and 9 as well as the most effective anti‐proliferative agent towards multiple human cancer cell lines. The cellular mode of action of this compound was investigated in MV4‐11 acute myeloid leukaemia cells, revealing that the compound dampened the kinase activity of cellular CDKs 7 and 9, arrested the cell cycle at sub‐G1 phase and induced apoptosis.