We measured the properties of a novel combination of two Gas Electron Multipliers with a Micromegas for use as amplification devices in high-rate gaseous time projection chambers. The goal of this design is to minimize the buildup of space charge in the drift volume of such detectors in order to eliminate the standard gating grid and its resultant dead time, while preserving good tracking and particle identification performance. To characterize this micro-pattern gas detector configuration, we measured the positive ion back-flow and energy resolution at various element gains and electric fields, using a variety of gases, and additionally studied crosstalk effects and discharge rates. At a gain of 2000, this configuration achieves an ion back-flow below 0.4% and an energy resolution better than σ/E=12% for 55Fe X-rays.