The development of an objective technique for identifying significant hidden frequencies in the spectrum makes it possible to accurately predict shallow-water tides by harmonic methods. For Anchorage, Alaska, the 114 constituents used include frequencies in every species (cycles per day) from 0 to 12. The larger set of constituents improved the predictions in times of high and low waters, range of tide, and shape of curve. The stationary characteristics of some of the added constituents have been tested with three years of Philadelphia data.