They once pulled the strings of Israel's economy, but now the country's most influential tycoons are reeling under a popular backlash against corporate power and selling assets in a regulatory squeeze.

For investors willing to wade into a market in the middle of a dramatic overhaul, there is a rare opportunity to snatch up companies, from insurers to oil refineries, at bargain prices.

About a decade ago, as Israel's corporate debt market was just getting started, there was little oversight and risk taking was encouraged. A small number of tycoons used debt to expand their conglomerates into tiered corporate structures with cascading control over huge chunks of the economy.

By 2010, 10 large business groups controlled 30 percent of the market value of public companies, while 16 controlled half the money in the entire country.

The following year hundreds of thousands of Israelis took to the streets to protest against the high cost of living, and they pointed their fingers at the high concentration of corporate power.

"There is no question that in the past, these - let's call them tycoons - they had personal relationships with the managers or the chairmen of the banks. And this enabled them to get credit," said Ben-Zion Zilberfarb, an economics professor at Israel's Bar Ilan University.

After the 2011 protests, the banks started clamping down. When markets soured, a handful of them were stuck with tremendous debt.

Four years on, high-profile moguls can still feel the heat.

In July, Nochi Dankner, who through holding company IDB controlled Israel's largest supermarket chain and cellphone operator - Shufersal and Cellcom - and other businesses including a small airline, was sentenced to jail for manipulating share prices to try to save his crumbling empire.

Diamond dealer Lev Leviev, while busy negotiating a haircut with debtors, had to pay 550 million shekels ($146 million) from his own pocket last month to buy control of ailing Russia-focused real estate firm AFI Development from his holding company Africa Israel Investments.