A method and structure for reducing chip carrier flexing during thermal cycling. A semiconductor chip is coupled to a stiff chip carrier (i.e., a chip carrier having an elastic modulus of at least about 3×105 psi), and there is no stiffener ring on a periphery of the chip carrier. Without the stiffener ring, the chip carrier is able to undergo natural flexing (in contrast with constrained flexing) in response to a temperature change that induces thermal strains due to a mismatch in coefficient of thermal expansion between the chip and the chip carrier. If the temperature at the chip carrier changes from room temperature to a temperature of about −40° C., a maximum thermally induced displacement of a surface of the chip carrier is at least about 25% less if the stiffener ring is absent than if the stiffener ring is present. Since a propensity for cracking of the stiff chip carrier increases as the thermally induced displacement increases, the present invention, which avoids use of the stiffener ring, improves a structural integrity of the chip carrier.