Transient polymerization beyond the steady state has been experimentally observed in in vitro actin polymerization time courses. These 'polymerization overshoots' have previously been described in terms of the time-dependent probabilities for binding distinct nucleotide hydrolysis states within subunits near the plus ends of actin filaments. We demonstrate a different type of overshoot dynamics where the plus-end contribution to polymerization steadily decreases relative to that of the minus end. This decrease occurs due to plus-end capping of an initial impulse of rapidly created actin filaments. We calculate the contribution of these dynamics to observed overshoot magnitudes using rate equations describing the concentration of polymerized actin. We find this contribution is highly sensitive to both initial filament concentration and plus-end capping rate. We develop an analytic formula that describes the magnitude of the overshoot as a function of these two key parameters. The overshoots we describe could be observed by current experimental methods for studying the effects of severing and branching mechanisms upon actin polymerization in the presence of plus-end capping and rapid nucleotide exchange. We also present a plausible cellular mechanism that could greatly amplify these overshoots in vivo.