The disintegration of four radionuclides undergoing electron-capture decay was followed for one to ten half-lives. Least-squares analyses of the gamma-ray counting data using non-linear Taylor differential correction yielded the following half-lives: 7Be, 53.42±0.01 days; 54Mn, 312.6±0.5 days; 83Rb, 86.2±0.1 days and 84Rb, 33.1±0.1 days. These values are consistent with literature data, with comparable or much better precision than most previous determinations.