The present invention provides novel synthetic oligonucleotide sequences (hereinafter sequence) of 3 to 9 bases in length comprising one or more non-DNA bases wherein the bases are nebularine, hypoxanthine, or uracil, or combinations of nebularine, hypoxanthine and uracil bases. These sequences optionally further comprise one or more guanine bases or one or more thymine bases, or combinations thereof. The present invention also provides methods of using these compositions to induce responses in cells, and to treat diseases and conditions characterized by undesired cellular proliferation such as autoimmune disease, lymphoproliferative disease, inflammation or cancer.