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Electrically small antennas are generally presumed to exhibit high impedance mismatch (high VSWR), low efficiency, high quality factor (Q); and, therefore, narrow operating bandwidth. For an electric or magnetic dipole antenna, there is a fundamental lower bound for the quality factor that is determined as a function of the antenna's occupied physical volume. In this paper, the quality factor of a resonant, electrically small electric dipole is minimized by allowing the antenna geometry to utilize the occupied spherical volume to the greatest extent possible. A self-resonant, electrically small electric dipole antenna is presented that exhibits an impedance near 50 Ohms, an efficiency in excess of 95% and a quality factor that is within 1.5 times the fundamental lower bound at a value of ka less than 0.27. Through an arrangement of the antenna's wire geometry, the electrically small dipole's polarization is converted from linear to elliptical (with an axial ratio of 3 dB), resulting in a further reduction in the quality factor. The elliptically polarized, electrically small antenna exhibits an impedance near 50 Ohms, an efficiency in excess of 95% and it has an omnidirectional, figure-eight radiation pattern.