Low energy incomplete fusion has been studied in 12 C+ 159 Tb system at energies ≈ 4-7 MeV/nucleon. The excitation functions of individual reaction channels have been measured using off-line γ spectroscopy, and analyzed in the framework of statistical model code PACE4 based on the concept of equilibrated compound nucleus decay. A significant fraction of incomplete fusion has been found in the production of residues involving α particle(s) in the exit channels. For better insights into the onset and strength of incomplete fusion, the incomplete fusion strength function has been deduced as a function of various entrance channel parameters. Large influence of incomplete fusion has been observed at slightly above barrier energies, and increases smoothly with incident projectile energy. Present results have been compared with the results obtained in the interactions of 12 C with nearby targets to probe the dependence of incomplete fusion on entrance channel mass asymmetry. It has been found that the percentage fraction of incomplete fusion increases linearly with mass asymmetry of interacting partners in the studied mass region.