We designed MEF to mimic the basic region/helix-loop-helix/leucine zipper (bHLHZ) domain of transcription factors Max and Myc, which bind with high DNA sequence specificity and affinity to the E-box motif (enhancer box, CACGTG). To make MEF, we started with our rationally designed ME47, a hybrid of the Max basic region and E47 HLH, that effectively inhibited tumor growth in a mouse model of breast cancer. ME47, however, displays propensity for instability and misfolding. We therefore sought to improve ME47's structural and functional features. We used phage-assisted continuous evolution (PACE) to uncover "nonrational" changes to complement our rational design. PACE mutated Arg12 that contacts the DNA phosphodiester backbone. We would not have rationally made such a change, but this mutation improved ME47's stability with little change in DNA-binding function. We mutated Cys29 to Ser and Ala in ME47's HLH to eliminate undesired disulfide formation; these mutations reduced E-box binding activity. To compensate, we fused the designed FosW leucine zipper to ME47 to increase the dimerization interface and improve protein stability and E-box targeting activity.This "franken-protein" MEF comprises the Max basic region, E47 HLH, and FosW leucine zipper-plus mutations that arose during PACE and rational design-and is a tractable, reliable protein in vivo and in vitro. Compared with ME47, MEF gives three-fold stronger binding to Ebox with four-fold increased specificity for E-box over nonspecific DNA. Generation of MEF demonstrates that combining rational design and continuous evolution can be a powerful tool for designing proteins with robust structure and strong DNA-binding function.