The present invention provides a method for transforming an insect genome that has a much enhanced transformation frequency. The vectors and plasmids employed in the method are further described as transposition vectors that include a minimal amount of nucleotide sequence homologous to a 5’ region and a 3’ region of a native piggyBac nucleic acid sequence. The transformed cells or embryos may also be developed into transgenic organisms. Disclosed are minimal piggyBac-based plasmid constructs that comprises a minimal nucleic acid sequence homologous to a 5’ end of a piggyBac nucleic acid sequence (about 60-80 bp, particularly 66 bp) and a relatively long (300 to about 380 bp, particularly 311 bp or 378 bp) continuous nucleic acid sequence homologous to a 3’ end of a piggyBac native nucleic acid sequence. Methods employing these constructs include the use of a helper plasmid. Transformation frequencies employing the constructs are enhanced 100-fold or higher over that transformation frequency obtained using other than the herein described constructs.