In this study, correlations are developed to predict compression index (Cc) from index parameters so that one can be able to model Jimma soils with compression index using simple laboratory tests. Undisturbed and disturbed soil samples from twelve different locations in Jimma town were collected. Laboratory tests like specific gravity, grain size analysis, Atterberg limit, and one-dimensional consolidation test for a total of twenty-four test samples were conducted. From one-dimensional consolidation tests, compressibility soil parameters (Cc and Cs) are determined. From the results of limited tests, an indicative good correlation is observed between Cc and LL, PL, and PI. However, a Poor correlation is developed between Cc and PL when related to the other parameters. The developed correlations will be important inputs in modeling Jimma clay soils with regression model and Artificial neural networks (ANN) analysis using simple index tests. In addition, the results of this study can serve as a basis for further study of such correlations on different clay soils in the country. In this study, regression analysis was used to explore the significance of individual independent (index) soil properties. Regression model and correlation of compression index for liquid limit, plastic limit, and plasticity index were obtained from the linear regression analysis and ANN. This correlation will be helpful for geotechnical engineers in developing the coefficient of compression (Cc) value of expansive/clay soil from index properties. Finally, based on the general findings of the study, suitable recommendations have been forwarded.