Washing of antibody-agarose beads complex:
Multiple times of washing can eliminate the non-specific binding. Typically, washing buffer has the same ingredients as lysis buffer excluding glycerol, beacause the viscosity of glycerol would enhance non-specific binding.
For different experimental purposes, concentrations of NaCl and detergent can be adjusted to get a best eliminating of non-specific binding. For example, for a simple immunoprecipitation (not Co-IP) or a Co-IP with a relatively tight protein-protein binding, you can use low-concentration (0.2-0.5%) of SDS as a detergent to eliminate most of non-specific binding.