Six weeks after his high-profile effort to force California cities to increase housing density failed in the Legislature, the Democratic lawmaker behind the proposal introduced on Monday what he called a “light touch” approach — still pushing for more housing units in many single-family neighborhoods while also offering other communities the ability to skip lengthy environmental review for larger projects.

The bill by state Sen. Scott Wiener (D-San Francisco) would allow construction of duplex, triplex and fourplex residential units without additional local government approval in single-family neighborhoods using what’s known as “by-right” provisions of state law. The number of units that could be built would depend on the size of the city, with fourplex projects aimed at cities with a population greater than 50,000.