The epicenter of the economic meltdown we're still recovering from was part and parcel a result of a broken housing system. It's no surprise, then, that just about every company associated with the sector has been hurting dearly for the past few years.

But things may start changing, if only a little, in 2012. Below, I'll tell you one company to consider buying before things pick up again, and one to sell before it's too late.

Soon or later, a shrinking spread
The stock on my chopping block is Invesco Mortgage Capital (NYSE: IVR), a mortgage REIT that has several marks against it in my book. First and foremost among these is the fact that Invesco has a significant portion -- about 29% -- of its assets tied up in mortgages that aren't guaranteed by the federal government through Fannie, Freddie, or Ginnie.

On top of that, Invesco is far more leveraged than industry peers that also don't have 100% of their securities backed by the government. For instance, Chimera (NYSE: CIM), which has 53% of assets not backed by the government, is only levered 2.9 times, versus Invesco's 7.3 times leverage.

But most importantly, like other REITs, Invesco's ability to profit is based largely on the interest rate spreads it is able to benefit from. Borrowing money at low short-term interest rates and ensuring income from higher long-term rates is the company's bread and butter.  

That's where the Fed's Operation Twist plan comes in.

As fellow Fool John Maxfield points out, "The intended result of Operation Twist ... is to force short-term interest rates up and long-term interest rates down. That will narrow the interest rate spread that REITs rely on to make money and pay a generous dividend."

Though it may take awhile for those effects to filter through to investors, I'd hate to be holding shares when that day comes.

A burgeoning recovery?      
On the flip side of the housing coin is a company whose future I believe is very bright: Lumber Liquidators (NYSE: LL). The company has suffered over the past few years thanks to both the rough housing market and a botched conversion of its information management system. But I believe the stars may now be aligning.

As Fool Morgan Housel pointed out recently, "... housing is as unsustainably low right now as it was unsustainably high during the bubble years. ... Today we're building 500,000 homes a year while adding around 1 million new households per year."

Sooner or later, something is going to give, and the housing market will start its recovery. With a laser focus on hardwood flooring, Lumber Liquidators should easily be able to outmaneuver behemoths Home Depot (NYSE: HD) and Lowe's (NYSE: LOW).

These two megastores have far more to focus on than just hardwood flooring. In fact, mom-and-pop stores control two-thirds of the flooring market.  But with Lumber Liquidators' cost advantages through scale, super-low overhead structure, and superior value proposition, the opportunity for consolidation of this fragmented market represents a real runway for growth.

If you don't believe me, consider this: Lumber Liquidators currently owns just 12% of the flooring market. It is expanding at a breakneck pace, with 40 to 42 new stores opened in 2011. With the number of independent stores declining nationwide, it's easy to see how any improvement in housing could super-charge shares of Lumber Liquidators.

The ball is in your court
Let me know below if you agree with my thesis on these two companies. I'll be holding myself accountable on my profile, making a positive CAPScall on Lumber Liquidators and a negative one on Invesco.

And if you're a dividend investor who thinks Invesco's worrisome 17.3% dividend yield might not be for you anymore, worry not! We've prepared a special free report on 11 rock-solid dividend stocks for your consideration. Hand-picked by Motley Fool analysts, these selections represent the best of the best among dividend payers. Get your copy of the report today, absolutely free.