Planarizing solutions, planarizing machines and methods for planarizing microelectronic-device substrate assemblies using mechanical and/or chemical-mechanical planarizing processes. In one aspect of the invention, a microelectronic-device substrate assembly is planarized by abrading material from the substrate assembly using a plurality of first abrasive particles and removing material from the substrate assembly using a plurality second abrasive particles. The first abrasive particles have a first planarizing attribute, and the second abrasive particles have a second planarizing attribute. The first and second planarizing attributes are different from one another to preferably selectively remove topographical features from substrate assembly and/or selectively remove different types of material at the substrate surface.