Under the Brady law, law-enforcement officials have five days to search the background of a potential gun buyer.
New York, for instance, requires gun buyers to obtain permits, which can take months.
"A lot of the same names keep showing up as gun buyers," Stoddard said.
The four-day waiting period is meant to function something like the one imposed on gun buyers.
Dealers would be required to maintain gun buyers' paperwork for only a single day, rather than the law's current 90 days.
Such a measure would require dealers to request background information on prospective gun buyers.
When they arrive, Watts has begun a transaction with a gun buyer.
Last year in California, nearly 6,000 would-be gun buyers - most of them convicted criminals - were turned down.
In 2001, Davis signed a bill requiring gun buyers to pass a safety test.
Another new law restricts gun buyers to one weapon purchase per month.