A process for converting a tertiary halogenated hydrocarbons in a tertiary halogenated hydrocarbon-containing stream to a corresponding unhalogenated or less-halogenated unsaturated hydrocarbon product with the release of hydrogen halide involves contacting the tertiary halogenated hydrocarbon with a sorbent-type dehydrohalogenation catalyst in a reaction zone and optionally passing a stripping gas through the reaction zone to remove vapor phase reaction products from the reaction zone. A process for removing a tertiary chlorinated hydrocarbon impurity from 1,3-dichloro-1-propene involves contacting a mixture containing the 1,3-dichloro-1-propene and the tertiary chlorinated hydrocarbon impurity with a dehydrochlorination catalyst effective to catalyze a conversion of the tertiary chlorinated hydrocarbon impurity to a corresponding unchlorinated or less-chlorinated unsaturated hydrocarbon and hydrogen chloride and distilling the 1,3-dichloro-1-propene to produce a purified cis-1,3-dichloro-1-propene fraction and a purified trans-1,3-dichloro-1-propene fraction.