The distribution of rain along the radio propagation path is inhomogeneous. The non-uniformity of rainfall in both the horizontal and vertical directions makes the estimation of slant path attenuation complex. At frequencies above 10 GHz, the effects of attenuation and noise induced by atmospheric gases and rain are quite significant. Rain height data were obtained from the Tropical Rainfall Measuring Mission (TRMM) and NigComSat-1 satellite for 37 stations in Nigeria as reported in the literature. These TRMM and Nigeria data were used to find relationship between the rainfall rate and the effective slant path length. This effective length was used with local parameters at Universiti Teknologi Malaysia (UTM) to estimate the slant path attenuation values at the Ku-band. Furthermore, terrestrial attenuation data at 0.01% of the time for UTM were obtained from the UTM Wireless Communication Centre (WCC). Again, these attenuation data were transformed to slant path attenuation values using a transformation technique available in the literature. The attenuation exceeded for other percentages of the time was also obtained. The breakpoint model along with the ITU-R, DAH, Crane, Mandeep and the proposed modified ITU-R models were considered. It was observed that the validation results at 12 GHz clearly suggested that the proposed modified ITU-R model's estimates seem to provide fairly more acceptable results when compared with other models of interest.