Fears China's debt mountain will turn into an avalanche have hit the headlines recently, but there are signs at least some of the risk is easing.

That's in part due to the mainland's efforts to restructure its huge pile of local government debt, Moody's Investors Service said in a Monday report.

Nicholas Zhu, senior analyst at Moody's, said, "For the local government direct debt, we believe the government is finding a handle by capping it at 16 trillion yuan (Exchange: CNY=) ($2.45 trillion) overall and improving the structure by swapping some existing debt into bonds at lower cost and longer maturity."

If 2016 bond issuance remained steady at the 3.8 trillion yuan issued in 2015, Moody's estimated that about 54 percent of regional and local governments' (RLGs) direct debt would be shifted into bonds paying lower interest and with longer maturities and away from bank loans and financing vehicles.

Provincial governments' debt, often issued via local government financing vehicles, or LGFVs, has worried economists for years.

Outstanding debt climbed to around 17.9 trillion yuan by the end of the first half of 2013, according to the most recently released national audit results, from around 10.7 trillion in 2010. The results of a more recent national debt audit have not been released.

In late 2014, China's State Council, its highest authority, set quotas on the amount of debt that local governments could issue -- the 16 trillion yuan cap -- required the funds raised to be used for public projects rather than operational spending and tied debt levels to local officials' performance reviews.

The State Council also barred local governments from using LGFVs and state-owned enterprises (SOEs) to raise debt and from guaranteeing or covering the liabilities of financial institutions or local corporates.

Moody's Zhu noted that the 2016 bond issuance plan would also raise RLG disclosure standards, requiring the release of annual budget revenue and expenditure for 2014-16 with the issuance.

Moody's doesn't expect local governments, particularly upper-tier governments, provinces and main cities, to default on bonds issued in their own name, calling the probability "quite low."

So far, the bonds are finding buyers among commercial banks as well as asset managers and institutional investors, such as insurance companies, Zhu noted, adding that earlier this month, the central bank said it would allow qualified individual investors to buy and sell the bonds through commercial banks.

But the local government debt risk hasn't entirely faded. While there appeared to be a better handle on the direct debt, other liabilities - such as LGFVs and local state-owned enterprises' (SOE) debt - aren't as well defined, Zhu noted.