Dynamical atmosphere models were calculated for a large grid of variables with Mira-like properties satisfying the Iben radius-luminosity-mass relationship for evolving AGB stars. Their masses ranged from 0.7 to 2.4 M., and their periods from 150 to 800 days. All were fundamental-mode pulsators, had solar metallicity, and included effects of dust. As a natural consequence of evolutionary changes in stellar parameters, the mass-loss rate increases as an approximately exponential function of time, reaching -M approximately 10(-5) - 10(-4) M. yr-1. Further evolution is dominated by the powerful wind, which strips the star's envelope from the core. This " superwind " is a remarkably robust effect. It occurs for all initial stellar masses and all modeling parameters that have been tested. Dust promotes the effect but is not essential for it. Models with very low metallicity also show the effect, but at higher luminosities, which has intriguing implications for the number of supernovae in early low-metallicity populations and for the chemical evolution of galaxies.