Chemically strengthened glass articles having at least one deep compressive layer extending from a surface of the article to a depth of layer DOL of about 130 μm up to about 175 μm or, alternatively, to a depth of compression (DOC) in a range from about 90 μm to about 120 μm within the article. The compressive layer has a stress profile that includes a first substantially linear portion extending from a relatively shallow depth to the DOL or DOC and a second portion extending from the surface to the shallow depth. The second portion is substantially linear at a depth from 0 μm to 5 μm and has a steeper slope than that of the first portion of the profile. Methods of achieving such stress profiles are also described.