Charge-changing and fragment production cross sections at 0 degrees have been obtained for interactions of 290, 400, and 650 MeV/nucleon 40Ar beams, 650 and 1000 MeV/nucleon 35Cl beams, and a 1000 MeV/nucleon 48Ti beam. Targets of C, CH2, Al, Cu, Sn, and Pb were used. Using standard analysis methods, we obtain fragment cross sections for charges as low as 8 for Cl and Ar beams, and as low as 10 for the Ti beam. Using data obtained with small-acceptance detectors, we report fragment production cross sections for charges as low as 5, corrected for acceptance using a simple model of fragment angular distributions. With the lower-charged fragment cross sections, we cancompare the data to predictions from several models (including NUCFRG2, EPAX2, and PHITS) in a region largely unexplored in earlier work. As found in earlier work with other beams, NUCFRG2 and PHITS predictions agree reasonably well with the data for charge-changing cross sections, but do not accurately predict the fragment production cross sections. The cross sections for the lightest fragments demonstrate the inadequacy of several models in which the cross sections fall monotonically with the charge of the fragment. PHITS, despite not agreeing particularly well with the fragment production cross sections on average, nonetheless qualitatively reproduces somesignificant features of the data that are missing from the other models.