An in vitro method, using isolated proteins, for joining two double strand (ds) DNA molecules of interest, comprising: providing a first dsDNA molecule and a second dsDNA molecule which share a region of sequence identity at an end on each DNA molecule; and contacting the two DNA molecules simultaneously with: (a) a purified non-processive 5' exonuclease; (b) a purified single stranded DNA binding protein which accelerates nucleic acid annealing; (c) a purified non strand-displacing DNA polymerase, wherein the 5' exonuclease and the DNA polymerase are different entities; and (d) a purified ligase, under conditions whereby: a 3' single-stranded overhang is generated in each molecule by the exonuclease without the use of a restriction enzyme; the two single-stranded overhangs anneal to form a gapped molecule; the gaps are filled in by the polymerase; and nicks are sealed by the ligase, thereby joining the molecules and forming an intact double stranded DNA molecule, in which a single copy of the region of sequence identity is retained, wherein none of the enzymatic reactions is actively terminated prior to beginning another of the reactions. providing a first dsDNA molecule and a second dsDNA molecule which share a region of sequence identity at an end on each DNA molecule; and contacting the two DNA molecules simultaneously with: (a) a purified non-processive 5' exonuclease; (b) a purified single stranded DNA binding protein which accelerates nucleic acid annealing; (c) a purified non strand-displacing DNA polymerase, wherein the 5' exonuclease and the DNA polymerase are different entities; and (d) a purified ligase, under conditions whereby: a 3' single-stranded overhang is generated in each molecule by the exonuclease without the use of a restriction enzyme; the two single-stranded overhangs anneal to form a gapped molecule; the gaps are filled in by the polymerase; and nicks are sealed by the ligase, thereby joining the molecules and forming an intact double stranded DNA molecule, in which a single copy of the region of sequence identity is retained, wherein none of the enzymatic reactions is actively terminated prior to beginning another of the reactions. (a) a purified non-processive 5' exonuclease; (b) a purified single stranded DNA binding protein which accelerates nucleic acid annealing; (c) a purified non strand-displacing DNA polymerase, wherein the 5' exonuclease and the DNA polymerase are different entities; and (d) a purified ligase, under conditions whereby: a 3' single-stranded overhang is generated in each molecule by the exonuclease without the use of a restriction enzyme; the two single-stranded overhangs anneal to form a gapped molecule; the gaps are filled in by the polymerase; and nicks are sealed by the ligase, thereby joining the molecules and forming an intact double stranded DNA molecule, in which a single copy of the region of sequence identity is retained, wherein none of the enzymatic reactions is actively terminated prior to beginning another of the reactions. a 3' single-stranded overhang is generated in each molecule by the exonuclease without the use of a restriction enzyme; the two single-stranded overhangs anneal to form a gapped molecule; the gaps are filled in by the polymerase; and nicks are sealed by the ligase, thereby joining the molecules and forming an intact double stranded DNA molecule, in which a single copy of the region of sequence identity is retained, wherein none of the enzymatic reactions is actively terminated prior to beginning another of the reactions.