Described are methods for processing microelectronic device substrates by a lapping step, e.g., a final lapping step, wherein the step includes the use of an elastomeric pressure-sensitive adhesive to secure the microelectronic device substrate to a carrier that holds the substrate to a surface of the carrier during the lapping step, and wherein the pressure-sensitive adhesive can be a non-polysilicone based adhesive having mechanical properties that include a tan delta that is below about 0.2.