We reconstruct atmospheric levels of methyl bromide (CH3Br), methyl chloride (CH3Cl), chloroform (CHCl3), and dichloromethane (CH2Cl2) back to before 1940 using measurements of air extracted from firn on Law Dome in Antarctica. The firn air at this site has a relatively narrow age spread, giving high time resolution reconstructions. The CH3Br reconstructions confirm previously measured firn records but with more temporal structure. Our CH3Cl reconstruction is slightly different from previous reconstructions, raising some questions about CH3Cl in the firn. Our reconstructions for CHCl3 and CH2Cl2 are the first published records of concentration prior to direct atmospheric measurements. A two-box atmospheric model is used to investigate the budgets of these gases. Much of the variation in CH3Cl can be explained by biomass burning emissions that increase up to 1980 and then are relatively stable apart from some high burning years such as 1997--1998. The CHCl3 firn reconstruction suggests that the anthropogenic source for CHCl3 is greater than previously thought, with human influence on the soil source a possible important contributor here. The CH2Cl2 firn reconstruction is consistent with industrial emission estimates based on audited sales data but suggests that the ocean source of CH2Cl2 is less than previously estimated.