An analytical solution of the recursion formula for convolution of a sum‐of‐exponentials fluorescence impulse (&dgr;) response with an apparatus response (‘‘lamp’’) function approximated locally by a general polynomial of thenth degree is derived. The five lowest approximations are tested by comparison with properly simulated fluorescence evolution‐and‐decay data. These were obtained byanalyticalconvolution of selected &dgr; responses with ananalyticallydefinedapparatus function chosen closely to simulate typically observable flash‐lamp apparatus functions, taking account of the integration within channels inherent in the experimental collection of both ‘‘lamp’’ and fluorescence response curves. A precise comparison of the recovery of various test theoretical mono‐ and sum‐of‐exponentials impulse‐response parameters for the different approximations was attained by performing all calculations for both simulation and nonlinear least‐squares optimization analysis in double precision. The results highlight the advantages of using local higher‐order polynomial approximations under various circumstances. The improved time resolution in particular suggests more expedient regimes of data collection than heretofore possible.