Experimental results on the onset of incomplete fusion at slightly above barrier energies are discussed in this paper. Spin-distributions of evaporation residues populated via complete and/or incomplete fusion of 12C,16O (Elab ≈ 4–7 MeV) with 169Tm have been measured to probe associated ℓ–values. Particle (Z=1,2) – γ – coincidence technique has been used for channel selection. Entirely different entry state spin populations have been observed during the de-excitation of complete and incomplete composites. The complete fusion residues are found to be strongly fed over a broad spin range. While, a narrow range feeding for only high spin states has been observed in case of incomplete fusion residues. In the present work, incomplete fusion is shown to be a promising tool to populate high spin states in final reaction products. For better insight into the onset and strength of incomplete fusion, the relative contributions of complete and incomplete fusion have been deduced from the analysis of excitation functions and forward recoil ranges. A significant fraction of ICF has been observed even at energy as low as ≈ 7% above the barrier. The relative strengths of complete and incomplete fusion deduced from the analysis of forward-recoil-ranges and excitation functions complement each other. All the available results are discussed in light of the Morgenstern’s mass-asymmetry systematics. Incomplete fusion fraction is found to be large for more mass-asymmetric systems for individual projectiles, which points towards the projectile structure effect on incomplete fusion fraction. Experimentally measured forward ranges of recoils complement the existence of incomplete fusion at slightly above barrier energies, where more than one linear-momentum-transfer components associated with full- and/or partial-fusion of projectile(s) have been observed. Present results conclusively demonstrate the possibility to selectively populate high spin states via incomplete fusion.