JUNEAU, Alaska (AP) — Gov. Bill Walker on Wednesday signed into law state spending bills, rejecting funding for a south-central Alaska bridge project and for a vitamin D deficiency study.

Walker vetoed $2.5 million for the dormant Knik Arm crossing project, which would connect Anchorage to land in the fast-growing Matanuska-Susitna Borough. He had ordered a halt on new spending on that project years ago.

He also axed a roughly $500,000 study aimed at determining the prevalence of vitamin D deficiencies in pregnant women and babies. Walker said a similar study is ongoing.

The state has been trying to whittle down what once was a multibillion-dollar budget deficit blown open by low oil prices. Prices have started to rebound, and lawmakers, after several years of gridlock, this year agreed to use earnings from Alaska's oil-wealth fund, known as the Alaska Permanent Fund, to help fill the gap.

Walker's budget director, Pat Pitney, said the deficit has shrunk to about $700 million, which would be covered using savings. Oil prices will influence the ultimate size of that deficit.

Republican lawmakers, particularly in the House, sought more spending cuts. But Walker, in an interview, said he's comfortable with the current level of spending and with the increased funding planned for public safety and education.

Credit rating agency S&P Global recently revised its credit outlook for the state from negative to stable, noting passage of the permanent fund legislation and better oil prices.

Walker also supported setting at $1,600 the size of the dividend check that Alaska residents will receive this year from permanent fund earnings. That amount is about $1,050 less than Alaskans would have received had a formula for calculating dividends in state law been followed. This is the third straight year the calculation hasn't been followed.

Legislative leaders have said there was insufficient support for a full dividend this year. Some lawmakers saw paying a full dividend as fiscally reckless.

Walker on Wednesday also signed legislation calling for limited, structured withdrawals from Alaska Permanent Fund earnings to help pay government costs. The bill leaves up to future legislatures how to distribute withdrawals between government costs and the dividend.

During legislative debate on the bill, Sen. Bill Wielechowski, an Anchorage Democrat, called the measure meaningless and said the rules it lays out could be ignored.

The new fiscal year starts July 1.