We explore the relationship between the morphology and ionic conductivity of block copolymer electrolytes over a wide range of salt concentrations for the system polystyrene-block-poly(ethylene oxide) (PS-b-PEO, SEO) mixed with lithium bis(trifluoromethanesulfonyl)imide salt (LiTFSI). Two SEO polymers were studied, SEO(16-16) and SEO(4.9-5.5), over the salt concentration range r = 0.03-0.55. The numbers x and y in SEO(x-y) are the molecular weights of the blocks in kg mol(-1), and the r value is the molar ratio of salt to ethylene oxide moieties. Small angle X-ray scattering was used to characterize morphology and grain size at 120 degrees C, differential scanning calorimetry was used to study the crystallinity and the glass transition temperature of the PEO-rich microphase, and ac impedance spectroscopy was used to measure ionic conductivity as a function of temperature. The most surprising observation of our study is that ionic conductivity in the concentration regime 0.11 <= r <= 0.21 increases in SEO electrolytes but decreases in PEO electrolytes. The maximum in ionic conductivity with salt concentration occurs at about twice the salt concentration in SEO (r = 0.21) as in PEO (r = 0.11). We propose that these observations are due to the effect of salt concentration on the grain structure in SEO electrolytes.