The bacterial D-alanyl-D-alanine transpeptidases (DD-peptidases) are the killing targets of beta-lactams, the most important clinical defense against bacterial infections. However, due to the constant development of antibiotic-resistance mechanisms by bacteria, there is an ever-present need for new, more effective antimicrobial drugs. While enormous numbers of beta-lactam compounds have been tested for antibiotic activity in over 50 years of research, the success of a beta-lactam structure in terms of antibiotic activity remains unpredictable. Tipper and Strominger suggested long ago that beta-lactams inhibit DD-peptidases because they mimic the D-alanyl-D-alanine motif of the peptidoglycan substrate of these enzymes. They also predicted that beta-lactams having a peptidoglycan-mimetic side-chain might be better antibiotics than their non-specific counterparts, but decades of research have not provided any evidence for this. We have recently described two such novel beta-lactams. The first is a penicillin having the glycyl-L-alpha-amino-epsilon-pimelyl side-chain of Streptomyces strain R61 peptidoglycan, making it the "perfect penicillin" for this organism. The other is a cephalosporin with the same side-chain. Here, we describe the X-ray crystal structures of the perfect penicillin in non-covalent and covalent complexes with the Streptomyces R61 DD-peptidase. The structure of the non-covalent enzyme-inhibitor complex is the first such complex to be trapped crystallographically with a DD-peptidase. In addition, the covalent complex of the peptidyl-cephalosporin with the R61 DD-peptidase is described. Finally, two covalent complexes with the traditional beta-lactams benzylpenicillin and cephalosporin C were determined for comparison with the peptidyl beta-lactams. These structures, together with relevant kinetics data, support Tipper and Strominger's assertion that peptidoglycan-mimetic side-chains should improve beta-lactams as inhibitors of DD-peptidases.