A wringer, for example for mops, includes one or more positioning elements to position a mop at least in one dimension in the wringer, for example to a desired depth in the wringer, to wring the mop. The positioning elements far other than a bottom surface of the wringer. A wringer is also disclosed in which a wringing surface is moved toward another wringing or a base surface in a drawing or pulling motion. A wringer is also disclosed where the wringing operation can be activated by a pivoting or other mechanism that can be operated from at least two positions, a plurality of spaced apart locations, from handles, or by way of structures positioned outside of a wringing envelope defined by wringing plates or other components contacting a mop element. The structures can be used to operate the wringer even if a handle of a mop element extends outward of the wringing envelope.