The ionic conductivity of concentrated LiI-polyethylene oxide P(EO)n high surface area oxide composite polymer electrolytes has been investigated. Two different Arrhenius dependences for concentrated composite polymer electrolytes (CPEs) have been identified. The first one is characterized by an inflection point at about 80°C, and the second, by a conductivity jump. We have suggested that in CPEs, where 3 < n < 9, the solid phase is major contributor to the overall ionic conductivity at temperatures above, but close to the melting point of the eutectic (Tm < T < Tk), where Tk is the knee temperature. It is important to note that at T < Tk the apparent activation energy of conduction (Ea) for composite solid electrolytes (CSEs, n ≤ 3), is about 40% of that for CPEs. We believe that the preferred conduction path in even more concentrated CPEs, which are defined as CSEs, is interfacial conduction. Differential scanning calorimetry (DSC), scanning electron microscopy (SEM), and x-ray data, presented in this communication, are evidence supporting our view. The effects of several parameters including type and content of oxide matrix, Li salt to ethylene oxide (EO) ratio, copolymers, and solvents on polymer electrolyte conductivity (especially at T > Tk or Tjump) and on Ea have been studied (Tjump is a temperature of the conductivity jump). The addition of small quantities of ethylene carbonate (EC), poly(methyl methacrylate), and polyacrylonitrile were found to be beneficial while poly(methyl acrylate), poly(butyl acrylate), and poly(vinylidene fluoride) additions made the polymer electrolyte stiffer and less conductive. MgO, Al2O3, and potassium aluminosilicate muscovite mica based CSEs have similar conductivity. DSC and SEM results clearly demonstrated the depression of CPE crystallinity by addition of fine Al2O3 powder, ethylene carbonate, and poly(ethylene glycol) dimethyl ether. This is in agreement with the conductivity enhancement of the CPE.