This study evaluates different methods of strengthening existing square concrete columns under eccentric loading. Sixteen reinforced square concrete columns were cast. The columns were made from normal strength concrete and the reinforcement was kept at minimum simulating columns needing retrofitting. Four columns were modified with round comers and wrapped with three layers of CFRP, four were circularised by circular segments and wrapped with three layers of CFRP, and the last four columns were circularised and confined with steel straps. Specimens from each group were tested under concentric, eccentric (15 or 25 mm) and flexural bending. Results from the study showed that part-circular concrete covers dramatically reduce stress concentration at the comers. FRP wrapped columns with circular segments showed significant increase in load-carrying capacity compared to columns with only round comers. Columns confined with steel straps showed comparable increase in both ultimate load and ductility.