Relative rate experiments are used to measure rate constants and temperature dependencies of the reactions of OH with CH3F (41), CH2FCl (31), CH2BrCl (30B1), CH2Br2 (30B2), CHBr3 (20B3), CF2BrCHFCl (123aB1 alpha), and CF2ClCHCl2 (122). Rate constants for additional compounds of these types are estimated using an empirical rate constant estimation method which is based on measured rate constants for a wide range of halocarbons. The experimental data are combined with the estimated and previously reported rate constants to illustrate the effects of F, Cl, and Br substitution on OH rate constants for a series of 19 halomethanes and 25 haloethanes. Application of the estimation technique is further illustrated for some higher hydrofluorocarbons (HFCs), including CHF2CF2CF2CF2H (338pcc), CF3CHFCHFCF2CF3 (43-10mee), CF3CH2CH2CF3, (356ffa), CF3CH2CF2CH2CF3 (458mfcf), CF3CH2CHF2 (245fa), and CF3CH2CF2CH3 (365mfc). The predictions are compared with literature data for these compounds.