An improved service-life, low-profile, elastomeric mounting for placement between the side-frame-pedestal-jaw roof and the axle-box or axle-bearing adapter crown on a three-piece, railroad-car truck. The mounting minimizes the damaging compression induced edge strains resulting from the cocking motions imposed on the elastomeric mounting during railroad car braking and rocking. The addition of shims, specialized elastomer contouring, graded thicknesses of the elastomeric layers in combination with high shape factor of the elastomeric layers allows the compression induced edge strains to be significantly reduced and results in extended service-life of the elastomeric mounting.