IN THIS PAPER, WE CONSIDER METRIC VARIANTS OF HOMOGENEITY, COUNTABLE DENSE HOMOGENEITY (CDH), AND STRONG LOCAL HOMOGENEITY (SLH) BY REQUIRING THAT THE HOMEOMORPHISMS THAT WITNESS THE HOMOGENEITY ARE SOME TYPES OF ISOMETRIES OR LIPSCHITZ MAPS. THE STANDARD METHOD FOR PROVING THAT A SPACE IS CDH USES A THEOREM OF BENNETT (SEE [1]) WHICH STATES THAT COMPLETE SPACES ARE CDH WHENEVER THEY ARE SLH. AS THE MAIN RESULT WE GIVE A METRIC MODEL OF THIS THEOREM AND SHOW THAT EVERY BANACH SPACE IS LIPSCHITZ-CDH.