Two alpha-decaying isomeric states were observed in Po-191 with E-alpha = 7334(10) keV and T-1/2 = 22(1) ms for Po-191g and E-alpha = 7378(10) keV and T-1/2 = 98(8) ms for Po-191m. Evidence was found for fine-structure decay to excited levels in the Pb-187 daughter nucleus. The tentative interpretation of these new levels involves the weak coupling of the odd neutron to an intruder pi-(2p-2h) deformed 0(+) state in the even-even core. The long half-life of the Po-191m (Delta l = 0) alpha decay points to a deformed 13/(2)+ isomeric state in Po-191. [S0031-9007(99)08527-0].