Post-processing of additively manufactured (AM) aluminium alloy parts via laser polishing (LP) is particularly challenging due to the materials' high thermal conductivity, diffusivity, and reflectivity. Here, a novel multi-step laser polishing strategy, by combining laser ablation and smoothing steps, is developed that effectively reduces the surface roughness of AM AlSi10Mg parts. The minimum average roughness (Sa) and 10-point height (S10z) are achieved as 1.81 µm and 23.7 µm, representing maximum reductions of 94.1% and 89.8%, respectively, from the as-built AM surfaces (initial Sa 8 -28 µm). A strong relationship has been observed between the initial surface roughness and the achievable roughness reduction. Regarding the other surface integrity factors, sub-surface microhardness (between 10-40 µm) after LP increases up to 182 HV0.01, compared to the bulk hardness (105 HV0.01) measured ~60 µm below the surface. Clear evidence of material's flow within the surface asperities during the LP steps is observed from the cross-sectional microstructures. Further study will involve in-depth analysis of materials' compositions within the LP-processed layers.