Absorbable implants for breast surgery that conform to the breast parenchyma and surrounding chest wall have been developed. These implants support newly lifted breast parenchyma, and/or a breast implant. The implants have mechanical properties sufficient to support a reconstructed breast, and allow the ingrowth of tissue into the implant as it degrades. The implants have a strength retention profile allowing the support of the breast to be transitioned from the implant to regenerated host tissue, without significant loss of support. Three-dimensional implants for use in minimally invasive mastopexy/breast reconstruction procedures are also described, that confer shape to a patient's breast. These implants are self-reinforced, can be temporarily deformed, implanted in a suitably dissected tissue plane, and resume their preformed three-dimensional shape. The implants are preferably made from poly-4-hydroxybutyrate (P4HB) and copolymers thereof. The implants have suture pullout strengths that can resist the mechanical loads exerted on the reconstructed breast.