Described herein are methods and compositions that provide highly efficient nucleic acid amplification and signal detection using a cycling probe. In some embodiments, this allows a 3-fold or greater increase of amplification product for each amplification cycle and therefore increased sensitivity and speed over conventional PCR. Modified bases can be employed in primers to provide this base-3 or greater amplification with satisfactory PCR cycle times, which are improved, as compared to those observed in the absence of modified bases.