The Texas House gave a thumbs Wednesday to a bill allowing smaller homes on smaller lots in Texas’ biggest cities, part of a broad push by state lawmakers to put a dent in the state’s high home prices.

But the House made significant tweaks that would limit how many new homes could be built under the bill, setting up a potential showdown with the Texas Senate over one of Lt. Gov. Dan Patrick’s biggest priorities.

Senate Bill 15 would reduce how much land cities say single-family homes in new subdivisions must sit on. The idea is to let homebuilders construct homes on smaller amounts of land, thus reducing the overall price of the home.

“This bill allows the option of building homes at different types and price points to meet the demand and needs of buyers,” state Rep. Gary Gates, a Richmond Republican who carried the bill in the House, said during initial debate on the bill Tuesday. “Lowering the size and type of residential housing will increase the amount of housing that can be built and lowers housing costs.”

Initially, SB 15 would forbid major cities from requiring homes in new subdivisions to sit on more than 1,400 square feet as first proposed in the bill. Gates amended that provision Tuesday to 3,000 square feet. The state’s biggest cities tend to require single-family homes to sit on around 5,000 to 7,500 square feet of land, a Texas Tribune analysis found.

The provision would only apply in new subdivisions with at least five acres of land, and wouldn’t touch existing neighborhoods. The bill would only apply to cities with at least 150,000 residents in counties with a population of 300,000 or more — 19 of the state’s largest cities, per a Tribune analysis of U.S. Census Bureau data. It also wouldn’t apply in cases in which homeowners association and restrictive covenants prevent smaller lot sizes.

Wednesday’s 86-43 vote came after a dramatic turn of events at the tail end of the legislation in which a Democrat tried to kill the bill on a technicality, but supporters managed to revive it in time to reach the full House before a key deadline.

Some Democrats weren’t convinced the bill would tame housing costs — though evidence broadly suggests that homes on smaller lots have lower values than those on bigger lots. Some of them expressed uneasiness about the state weighing in on what kinds of homes can be built and where, a power the state grants to cities.