A novel instrument allows for the first time measurements of the lateral adhesion forces at a solid-liquid interface, f(parallel), in a way that is decoupled from the normal forces, f(perpendicular). We use it to measure how f(parallel) between a drop and a surface is influenced by different f(perpendicular) and different histories of drop resting periods on the surface prior to sliding, t(rest). The variation of f(parallel) with t(rest) is similar for different f(perpendicular) and always plateaus as t(rest)-->infinity. We show that the f(parallel) plateau value is higher when f(perpendicular) is lower. This seemingly counterintuitive result is in agreement with recent theories.