Federal and state policies on eligibility to purchase and possess firearms and background check requirements for firearm transfers are undergoing intensive review and, in some cases, modification. Our objective in this third report from the Firearms Licensee Survey (FLS) is to assess support among federally licensed firearms retailers (gun dealers and pawnbrokers) for a background check requirement on all firearm transfers and selected criteria for denying the purchase of handguns based on criminal convictions, alcohol abuse, and serious mental illness. The FLS was conducted by mail during June-August, 2011 on a random sample of 1,601 licensed dealers and pawnbrokers in 43 states who were believed to sell at least 50 firearms annually. The response rate was 36.9%, typical of establishment surveys using such methods. Most respondents (55.4%) endorsed a comprehensive background check requirement; 37.5% strongly favored it. Support was more common and stronger among pawnbrokers than dealers and among respondents who believed that "it is too easy for criminals to get guns." Support was positively associated with many establishment characteristics, including sales of inexpensive handguns, sales that were denied when the purchasers failed background checks, and sales of firearms that were later subjected to ownership tracing, and were negatively associated with sales at gun shows. Support for three existing and nine potential criteria for denial of handgun purchase involving criminal activity, alcohol abuse, and mental illness exceeded 90% in six cases and fell below 2/3 in one. Support again increased with sales of inexpensive handguns and denied sales and decreased with sales of tactical (assault-type) rifles. In this survey, which was conducted prior to mass shootings in Aurora, Colorado; Oak Creek, Wisconsin; Newtown, Connecticut; and elsewhere, licensed firearm sellers exhibited moderate support for a comprehensive background check requirement and very strong support for additional criteria for denial of handgun purchases. In both cases, support was associated with the intensity of respondents' exposure to illegal activities.