An objective method of estimating regional averages of coherent sea level (SL) change is developed. The technique is applied to a large set of SL data representative of most of the world's continental margins. The results show highly coherent SL changes over many of the regions studied. The method is then applied to the regional averages themselves to develop an overall estimate of the coherent pattern of SL variations existing in the historical SL data set. The pattern is characterized by a coherent rise of SL in all regions except Alaska, Scandinavia (both areas of notorious crustal uplift), and Southeast Asia, where SL appears to be falling. The analysis suggests little or no change in SL prior to the early 1900's. The period since that time has seen an increase in SL that is optimally fit by a linear trend of 23 cm/century. The study results suggest that it is not possible to uniquely determine either a global rate of change of SL or even the average rate of change associated with the existing (inadequate) data set. Indeed, different analysis methods, by themselves, can cause 50% variations in the estimates of SL trend in the existing data set. A signal/noise analysis suggests it should be easy to detect small, future changes in the SL trends estimated for the period 1930--1980. However, detection of theoretically predicted low-frequency signals (e.g., caused by CO2 warming) will be difficult in view of the huge, low-frequency, natural variability associated with glacial/tectonic processes.