We, at last, have two bills in Congress – one in the House and one in the Senate – addressing the long-festering problem of what to do with Fannie Mae and Freddie Mac and proposing a housing finance sector without them.

The Senate bill, introduced by Sens. Bob Corker, R-Tenn., and Mark Warner, D-Va., is self-consciously bipartisan and sets out with impressive success to give the maximum number of people something. The House bill, proposed by Financial Services Committee Chairman Jeb Hensarling, R-Texas, is a GOP bill that sets out to bring the advantages of much more robust private markets to housing finance.

The historical context of these bills is critical: the American housing finance system has collapsed in disgrace twice in three decades. A pretty poor record.

That we have learned something is apparent from a number of essential provisions that the two bills have in common.

Both bills would end Fannie and Freddie as government-sponsored enterprises. Both understand that the fundamental GSE model, which involves pretending to be simultaneously a private company and part of the government and results in privatized profits and socialized losses, is insidious and needs to be definitively terminated.

Both also understand that this large change must be phased in, so they phase out Fannie and Freddie over several years.

Both understand that we must have much more private capital bearing the credit risk of the mortgage market, that is, more private "skin in the game." Both go in the same direction here, although the House bill is better in that it goes further. That bill would take us to a housing finance sector which would be about 80% private and 20% government — about the optimal mix. But both bills unambiguously recognize that to have built a huge government-guaranteed system with so little skin in the game, as the U.S. did, was really stupid.

Both would end the affordable housing goals of the GSE system, and recognize that these goals, which are actually quotas, were a mistake, just as the fundamental GSE structure was a mistake.

Both bills propose, sensibly, to use the Federal Home Loan banks as mortgage aggregators and securitizers for small and midsize banks and credit unions. These institutions in general originate the highest credit quality mortgage loans. (I must confess that as the inventor of the FHLBs' mortgage programs, which are built on emphasizing originator skin in the game, I have a sentimental preference here.)

Neither of the bills has the least interest in having speculative investors in the old, junior preferred stock of Fannie and Freddie, or in their common stock, be rewarded by political action. As put in the form of a sharp-pointed rhetorical question by Corker: Who would pay Fannie or Freddie a penny of guarantee fees based on their own financial merit, if the government were not completely propping them up? Correct answer: Nobody—not one penny.

A final similarity of the two bills is that neither reflects one further essential lesson: the need for countercyclical standards which constrain the overleveraging of real estate in bubbly markets. The most efficient way to do this is by having countercyclical loan-to-value limits, so that as house prices soar to unsustainable levels, the allowable leverage is reduced. CCLTVs will moderate both bubbles and busts, and both bills would benefit from having this core concept added.

We need also to consider a few of the biggest differences between the bills.

The most prominent difference, of course, is that the Senate bill includes a full faith and credit government guarantee of mortgage-backed securities by a Federal Mortgage Insurance Corporation. This proposal is better than and, in particular, more honest than, the former foolish claims that Fannie and Freddie were not really guaranteed by the government. But it is still both unwise and unnecessary.

Proponents of the Corker-Warner bill support putting in this taxpayer risk as "balanced"—by which I think  they mean it makes happy many parties who enjoy subsidies from such guarantees. Proponents also say the government guarantee is only for catastrophes — and point out the bill's requirement that credit losses up to 10% of principal must be covered by private capital. This 10% skin-in-the-game requirement is distinctly better than Fannie and Freddie. Nonetheless, the existence of such a government guarantee will cause excess debt and excess leverage to flow to real estate. It will create a lot of creditors who do not care if they are financing increased asset price inflation and increased systemic risk. It will thereby make the very catastrophes it is supposed to protect against instead more likely to occur.

A second difference is that the House bill addresses the Federal Housing Administration as an integral part of the problem. It proposes the excellent idea of removing the FHA from the U.S. Department of Housing and Urban Development, and making it into a separate government corporation, with an arm's-length regulator. It would be much easier to see and understand what is going on in a separate corporation, as opposed to the current, opaque form of the FHA.

The House bill also provides for establishing the legal framework for an American-covered bond market. Covered bonds would give the banking sector an additional alternative for long-term financing of mortgages on a 100% skin-in-the-game basis.

Overall, it is a good start to have bills in both the House and Senate that agree on the main point of ending the disastrous political experiment of Fannie and Freddie.

Alex J. Pollock is a resident fellow at the American Enterprise Institute. He was president and CEO of the Federal Home Loan Bank of Chicago from 1991 to 2004.