The importance of Tandem Repeats in some genomes is now well established. We have reported elsewhere some interesting new results obtained by means of a preliminary program for finding Tandem Repeats in DNA sequences, together with a brief description of the basic ideas of the algorithm. We describe here a completely new program based only in part on those ideas, we briefly discuss the interpretation of the results, and, by way of example, we provide a few novel results relative to the parasites responsible of two re-emerging diseases, Plasmodium falciparum and Mycobacterium tuberculosis. Our program is portable, effective, powerful and fast: it can run on current desktop computers, and it finds all significant Tandem Repeats also in the longest segments of sequences in databases (up to millions of bases), in short times (minutes).