We explore the phase diagram and mechanical properties of molecular gels produced from mixing water with a dimethyl sulfoxide (DMSO) solution of the aromatic dipeptide derivative fluorenylmethoxycarbonyl-diphenylalanine (Fmoc-FF). Highly soluble in DMSO, Fmoc-FF assembles into fibrous networks that form gels upon addition of water. At high water concentrations, rigid gels can be formed at Fmoc-FF concentrations as low as 0.01 wt %. The conditions are established defining the Fmoc-FF and water concentrations at which gels are formed. Below the gel boundary, the solutions are clear and colorless and have long-term stability. Above the gel boundary, gels are formed with increasing rapidity with increasing water or Fmoc-FF concentrations. A systematic characterization of the effect of Fmoc-FF and water concentrations on the mechanical properties of the gels is presented, demonstrating that the elastic behavior of the gels follows a specific, robust scaling with Fmoc-FF volume fraction. Furthermore, we characterize the kinetics of gelation and demonstrate that these gels are reversible in the sense that they can be disrupted mechanically and rebuild strength over time.