With all the current focus on dependable dividend stocks among risk-averse investors, it can pay to take a longer look at stocks that do the opposite of what folks want now. How do companies fare after they cut their dividend?

Back in the March 2011 Smart Money, Jack Hough did just that. The result: “Surprisingly, dividend cuts tend to foretell a rebound in a company’s earnings.”

A couple of interesting points from the article before we get to test this premise on some new names:

• In 1989, there were 26 S&P 500 Dividend Aristocrats (companies that have increased dividend payments for 25 straight years), and in March 2011, less than one-quarter remained
• The average stay for a Dividend Aristocrat is 10 years
• The five-year average return (through March 2011) for the Dividend Aristocrats was 6.3% vs. the S&P’s 2.3% return.

Hough used data compiled by Thompson Reuters showing sales growth improvements at Nucor (NYSE:NU), General Electric (NYSE:GE), Pfizer (NYSE:PFE) and ConAgra (NYSE:CAG). All had previously cut their dividends and indeed, three of the four (not GE) had seen increased revenues afterward (unfortunately, the article didn’t actually examine earnings after the dividend cuts).

What this implies is that a dividend cut — which is virtually always considered a fairly drastic step to take — can force a company to tighten operations, reinvigorate sales and presumably earnings, prop up the cash flow and finally provide some needed pop to the share price.

If that’s the case, than the following three companies better start to hope that action taken is result accomplished, at least in the long term:

Clearly, each of these companies has work to do, perhaps none as much as J.C. Penney (NYSE:JCP), which has slashed nearly every expense item except for capital spending. CEO Ron Johnson’s attempt to rescue the iconic retailer is falling on hard times, but the dividend cut will at least save money for more capital improvements, and time will tell if it all works out.

Similarly, RadioShack (NYSE:RSH) appears to be on life support, and unless it can figure out a way to somehow latch on to a name-brand e-tailer like Amazon (NASDAQ:AMZN) or eBay (NASDAQ:EBAY) or anyone that can give it even a chance at selling goods online, it may be doomed. The good news is that at least the stock price is holding its own.

Last but not least is SuperValu (NYSE:SVU), which is battling for grocery shoppers on every level of the food chain, from Wal-Mart (NYSE:WMT) to Whole Foods (NASDAQ:WFM) to Dollar General (NYSE:DG). Again, a dividend cut will save money, but will the savings find a way to the shelves in time for better bargains for consumers?

Hough’s piece may have been prescient for at least two of the giants, Pfizer and GE, which have both managed to rebound fairly well from past dividend cuts (understand that GE had no choice due to some U.S. government pressure). But I don’t think the dividend cuts on these three companies will have the long-term impact management or investors hope for, and stock appreciation is limited at best.

But hey, you never know. And while we wait for some results, think about some other companies that should — as a possible last resort to save money and spend it more wisely — cut dividends.

You know, like Pitney Bowes (NYSE:PBI) or Avon (NYSE:AVP).

Marc Bastow is an Assistant Editor at InvestorPlace.com. As of this writing he is long GE.