The impact of micron-size drops on a smooth, flat, chemically homogeneous solid surface is studied using a diffuse-interface model (DIM). The model is based on the Cahn–Hilliard theory that couples thermodynamics with hydrodynamics, and is extended to include non-90° contact angles. The (axisymmetric) equations are numerically solved using a combination of finite- and spectral-element methods. The influence of various process and material parameters such as impact velocity, droplet diameter, viscosity, surface tension and wettability on the impact behaviour of drops is investigated. Relevant dimensionless parameters are defined and, depending on the values of the Reynolds number, the Weber number and the contact angle, which for the cases considered here range from 1.3 to 130, 0.43 to 150 and 45° to 135°, respectively, the model predicts the spreading of a droplet with or without recoil or even rebound of the droplet, totally or partially, from the solid surface. The wettability significantly affects the impact behaviour and this is particularly demonstrated with an impact at Re = 130 and We = 1.5, where for θ < 60° the droplet oscillates a few times before attaining equilibrium while for θ ≥ 60° partial rebound of the droplet occurs, i.e. the droplet breaks into two unequal sized drops. The size of the part that remains in contact with the solid surface progressively decreases with increasing θ until at a value θ ≈ 120° a transition to total rebound happens. When the droplet rebounds totally, it has a top-heavy shape.