Recent experimental and theoretical studies of femtosecond pump-probe pulse excitation of NaI have led to information concerning bound-state wave packet motion, the control of wave packet localization, and the control of the branching between photodissociation products. This paper reports calculations that (i) resolve the discrepancy between the experiments that employ 50-60 fs pulses and those that employ 150-175 fs pulses; the former experiments show that the wave packet motion changes from simple periodic to multiple periodic and back to simple periodic in a time span of 40 ps, while the latter experiments clo not show this change in wave packet dynamics; (ii) examine the relationship between pulse width and photodissociation yield; and (iii) determine the optimal nonlinear chirped pump pulse that best localizes the excited-state wave packet with prescribed position and momentum chosen to enhance the photodissociation yield.