A CMP method uses a slurry including a first metal oxide or semiconductor oxide particles (first oxide particles) in water. At least one particle feature is selected from (i) first oxide particles having a polydispersity >30%, (ii) a coating on first oxide particles including Group I or Group II ions, transition metal oxide, or organic material, (iii) first oxide particles mixed with fumed oxide particles, (iv) first oxide particles with average primary size >50 nm mixed with fumed oxide particles having average primary size 150 m2/gm. A substrate having an alumina surface is placed into a CMP apparatus, and CMP is performed with a rotating polishing pad and the slurry to polish the alumina surface.