This invention relates to methods that have been found useful in reducing non-specific binding in immunochemical assays, via methods that can be implemented much faster than those used by Ishikawa. The techniques include the use of a lipophilic bridge, such as a liposome, or the elution of the antigen-antibody complex from the solid phase by the use of an anti-idiotypic antibody or an antibody, or the use of a heterologous reversible bridge.