Alpha-decay of the new nuclide Bi-184 has been studied in the complete-fusion reaction Nb-93(Mo-94, 3n)Bi-184 at the velocity filter SHIP. The evaporation residues were separated in-flight and subsequently identified on the basis of recoil-alpha, recoil-alpha-gamma analysis and excitation functions measurements. Two alpha-decaying isomeric states in Bi-184 with half-life values of 13(2) ins and 6.6(1.5) ms were identified. The alpha-branching ratio of Tl-180 was deduced for the first time as, b(alpha) = (2-12)%. Improved data on the fine-structure alpha-decay of Bi-186 were obtained in the Nb-93(Mo-95, 2n)Bi-186 reaction. A similarity of the decay energies and half-life values of Bi-184,Bi-186 is pointed out and a possible explanation for this effect is suggested.