Over the past week, shares of waste- and water-management specialist Veolia Environmental (NYSE: VE) were up almost 20% -- not bad for a large company offering an outsized dividend yield.

If dedicated investors are willing to keep close tabs on it, Veolia could be a company that produces excellent results. Below, I'll cover the one crucial thing to keep your eye on if you're interested in this uber-high yielding company.

The executive suite and its strategic plan
As I covered a few weeks ago, there's been a lot of talk about the management at Veolia. In short, former CEO Henri Proglio spent his time as CEO -- 2003 to 2009 -- expanding Veolia's presence in waste and water management, as well as in transportation services.

The growth stretched the company's reach to over 70 countries. The problem, however, was that such moves left the company saddled with crippling debt at the worst possible time -- the global recession. Current CEO Antoine Frerot, tasked with righting the ship, decided that the company would need to sell off the transportation division, as well as exit about half the countries the company currently serves. 

Possibly feeling that his legacy was being assaulted, ex-CEO Proglio was rumored to want Frerot ousted at a February 29 board meeting. As I said then, if "Frerot is ousted for his smart, practical, and necessary business moves, Proglio will have only saved his ego -- and it could have dire consequences for shareholders."

Apparently, the market seems to agree with me. At the meeting on the 29th, the board not only supported Frerot's leadership by a wide margin, but also supported his restructuring plan. Following the announcement, shares traded up over 15%.

But there's more
Sadly, the story doesn't end there. Reuters reports that once French elections take place in May, the ouster may be on again -- since Proglio is friends with French president Nicolas Sarkozy.

Whispers of Frerot's possible ouster created an outcry in France that Sarkozy could not afford before election time. He even vehemently denied supporting the idea, saying the claim was "absurd." Apparently, that hasn't stopped speculation about a possible boardroom coup.

For investors who want exposure to the solid and steady business that waste management offers but aren't willing for all the drama surrounding Veolia, I still think Republic Services (NYSE: RSG) and Waste Management (NYSE: WM), with their strong dividend yields (over 3% and 4.1% respectively), are well-suited to such a spot in an investor's portfolio. In fact, fellow Fool Sean Williams outlines why Waste Management is a great buy right now.

But for those who like the world of high dividends, Veolia could well be worth the while – as long as you keep a keen eye on the situation with management.

If you're interested in a few more dividend ideas, I suggest you check out our special free report: "Secure Your Future With 11 Rock-Solid Dividends." To get the names of these eleven companies, read the report today, absolutely free!