In contrast to some of the recent investigations, this study shows that far less number of tide gauge stations experienced statistically significant accelerations in sea level rise during the 20^th century. Twenty-seven tide gauge stations with century long data were analyzed for the presence of an acceleration in global sea level rise using a kinematic model inclusive of a secular trend, acceleration, and compounded periodicities with autocorrelated random effects. Eight out of twenty-seven stations revealed statistically significant but slow sea level rise acceleration (p<0.01) within the 0.01-0.02 mm/yr² range compared to the sixteen stations with accelerations estimated using the models by the previous investigations,which did not account for the compounded periodicities and autocorrelations in sea level changes.