Antibody heavy chain (HC) and light chain (LC) variable region exons are assembled by V(D)J recombination. V(D)J junctional regions encode complementarity-determining-region 3 (CDR3), an antigen-contact region immensely diversified through non-templated nucleotide additions ("N-regions") by terminal deoxynucleotidyl transferase (TdT). HIV-1 vaccine strategies seek to elicit human HIV-1 broadly neutralizing antibodies (bnAbs), such as the potent CD4-binding site VRC01-class bnAbs. Mice with primary B cells that express receptors (BCRs) representing bnAb precursors are used as vaccination models. VRC01-class bnAbs uniformly use human HC VH1-2 and commonly use human LCs Vκ3-20 or Vκ1-33 associated with an exceptionally short 5-amino-acid (5-aa) CDR3. Prior VRC01-class models had non-physiological precursor levels and/or limited precursor diversity. Here, we describe VRC01-class rearranging mice that generate more physiological primary VRC01-class BCR repertoires via rearrangement of VH1-2, as well as Vκ1-33 and/or Vκ3-20 in association with diverse CDR3s. Human-like TdT expression in mouse precursor B cells increased LC CDR3 length and diversity and also promoted generation of shorter LC CDR3s via N-region suppression of dominant microhomology-mediated Vκ-to-Jκ joins. Priming immunization with eOD-GT8 60mer, which strongly engages VRC01 precursors, induced robust VRC01-class germinal center (GC) B cell responses. Vκ3-20-based responses were enhanced by N-region addition, which generates Vκ3-20-to-Jκ junctional sequence combinations that encode VRC01-class 5-aa CDR3s with a critical E residue. VRC01-class-rearranging models should facilitate further evaluation of VRC01-class prime and boost immunogens. These new VRC01-class mouse models establish a prototype for generation of vaccine-testing mouse models for other HIV-1 bnAb lineages that employ different HC or LC Vs.