Methods employing detergent compositions effective for reducing soil redeposition and accumulation on hard surfaces are disclosed. The alkaline detergent compositions employ vinylidene diphosphonic acid polymers, including unsaturated monocarboxylic acid polymers with a phosphonate end group, preferably a vinylidene diphosphonic acid end group, in combination with an alkali metal hydroxide or other alkalinity source. The alkaline detergent compositions preferably further employ threshold agents. The alkaline detergent compositions reduce the amount of phosphorus-containing materials and polyacrylate materials required for water conditioning, soil removal and soil antiredeposition.