Practical implementation of metal anodes in commercial lithium-ion batteries has been limited by the growth of dendritic protrusions, which can cause short-circuits and adversely affect battery safety. The impacts of the physical (such as external pressure and electrolyte shear modulus) and electrochemical (for example, conductivity, diffusivity and transference number) properties of a solid electrolyte on the propensity of lithium dendrite growth are investigated here. It is found that over a range of conditions, there are critical pressures above which growth of lithium dendritic protrusions can be prevented. The magnitude of this critical pressure depends on the elastic modulus of the electrolyte. Plastic deformation of lithium at high pressure results in reduced protrusion growth, which helps in obtaining stable deposition. For the first time, phase maps have been developed based on mechanical and transport properties of electrolytes, indicating conditions under which stable deposition of lithium is possible during long-term operation. Suppression of dendrites by individually altering conductivity, or diffusivity, or transference number, or elastic modulus of the electrolyte appears to be a relatively difficult task. Minor tailoring of the transference number and elastic modulus of present-day polymer electrolytes, in a combined fashion, can lead to dendrite-free deposition of lithium. (C) 2018 The Electrochemical Society.