Surface-enhanced Raman spectroscopy (SERS) is now a well-established technique for the detection, under appropriate conditions, of single molecules (SM) adsorbed on metallic nanostructures. However, because of the large variations of the SERS enhancement factor on the surface, only molecules located at the positions of highest enhancement, so-called hot-spots, can be detected at the single-molecule level. As a result, in all SM-SERS studies so far only a small fraction, typically less than 1%, of molecules are actually observed. This complicates the analysis of such experiments and means that trace detection via SERS can in principle still be vastly improved. Here we propose a simple scheme, based on selective adsorption of the target analyte at the SERS hot-spots only, that allows in principle detection of every single target molecule in solution. We moreover provide a general experimental methodology, based on the comparison between average and maximum (single molecule) SERS enhancement factors, to verify the efficiency of our approach. The concepts and tools introduced in this work can readily be applied to other SERS systems aiming for detection of every single target molecule.