The Universe appears to be expanding at an accelerating rate, driven by a mechanism called Dark Energy. The nature of Dark Energy is largely unknown and needs to be derived from observation of its effects. JEDI (Joint Efficient Dark-energy Investigation) is a candidate implementation of the NASA-DOE Joint Dark Energy Mission (JDEM). It will probe the effects of Dark Energy in three independent ways: (1) using Type Ia supernovae as cosmological standard candles over a range of distances, (2) using baryon acoustic oscillations as a cosmological standard ruler over a range of cosmic epochs, and (3) mapping the weak gravitational lensing distortion by foreground galaxies of the images of background galaxies at different distances. JEDI provides crucial systematic error checks by simultaneously applying these three independent observational methods to derive the Dark Energy parameters. The concordance of the results from these methods will not only provide an unprecedented understanding of Dark Energy, but also indicate the reliability of such an understanding. JEDI will unravel the nature of Dark Energy by obtaining observations only possible from a vantage point in space, coupled with a unique instrument design and observational strategy. Using a 2 meter-class space telescope with simultaneous wide-field imaging (~ 1 deg2, 0.8 to 4.2 μm in five bands) and multi-slit spectroscopy (minimum wavelength coverage 1 to 2 μm), JEDI will efficiently execute the surveys needed to solve the mystery of Dark Energy.