The alpha-decays of Xe-110 and Te-106 were studied at the GSI on-line mass separator. By using the grow-in and decay of the alpha activity, observed in pulsed-beam measurement, the half-life of Xe-110 was found to be T-1/2 = 105(-25)(+35) ms. The lifetime of Te-106 was determined to be T-1/2 = 70(-10)(+20) mus by measuring the time between two successive Xe-110 --> Te-106 --> Sn-102 alpha-decays. The newly determined half-lives were used to calculate reduced alpha-decay widths for Te-106 and Xe-110. Universal systematics of reduced alpha widths are proposed to search for the evidence of enhancement of the a formation amplitude in the emitters above Sn-100.