Smoluchowski's formalism yields, in the case of a two-dimensional system, unwieldy expressions for the time-dependent rate coefficient of a diffusion-controlled reaction and for the corresponding rate constant (which determines the rate of the reaction under stationary conditions). As a result, most kineticists have shunned the exact decay law and opted for facile alternatives, but the reliability of the ensuing results has not yet been put to a rigorous test. Two recipes, developed with an eye toward the pragmatics of data analysis, are presented and shown to lead, when applied to experimental data, to values of diffusion coefficient in agreement with those obtained by fitting the same data to the exact decay law.