Surface-tension-dominant droplet evaporation is ubiquitous and of importance to many applications. We present an improved Coupled Level Set and Volume of Fluid (i-CLSVoF) framework without explicit interface reconstruction for modelling micro-sized droplets with and without evaporation. In the i-CLSVoF framework, an improved surface tension force model with additional filtering steps to filter un-physical spurious velocities is developed and implemented. A simple, yet efficient, velocity-potential based approach is proposed to reconstruct a divergence-free velocity field for the advection of the free surface during droplet evaporation. This approach fixes the numerical issues resulting from the evaporation-induced velocity jump at the interface. The smeared mass source term approach incorporated in this work guarantees greater numerical stability than the non-smeared approach. Three different evaporation models (constant mass flux, thermally driven evaporation and droplet evaporation at room temperature) are implemented in the i-CLSVoF. Corresponding numerical benchmark cases (dam break, droplet relaxation and droplet evaporation subjected to different evaporation models) are conducted to validate the surface tension and the evaporation models. Good agreement between the numerical and corresponding analytical solutions is found. The model developed in this work shows convincing performance in modelling surface-tension-dominant flow with and without evaporation.