Why is it less effective to wash an insoluble precipitate with 15 ml of water once, than it is to wash the precipitate with 3 ml of water 5 times

I am thinking that when you wash an insoluble precipitate with water that the water will not be fully saturated with contaminants. Therefore, the concentration of contaminants would go down with each wash, whereas if you only washed it once with a larger volume of water, it would be less contaminated wash water.