We present a novel experimental method that solves two key problems in nondestructive mechanical studies of small biomolecules at the single-molecule level, namely the confirmation of single-molecule conditions and the discrimination against nonspecific binding. A biotin-avidin ligand-receptor couple is spanned between a glass slide and a 1 microm latex particle using short linker molecules. Optical tweezers are used to initiate bond formation and to follow the particle's thermal position fluctuations with nanometer spatial and microsecond temporal resolution. Here we show that each step in the specific binding process leads to an abrupt change in the magnitude of the particle's thermal position fluctuations, allowing us to count the number of bonds formed one by one. Moreover, three-dimensional position histograms calculated from the particle's fluctuations can be separated into well-defined categories reflecting different binding conditions (single specific, multiple specific, nonspecific). Our method brings quantitative mechanical single-molecule studies to the majority of proteins, paving the way for the investigation of a wide range of phenomena at the single-molecule level.