House Republicans are quietly moving ahead with dueling plans to replace the tax code with a simpler system. It’s a hot topic in advance of the April 15 filing deadline for individual income tax returns.

The latest budget blueprint from the chairman of the House Budget Committee, Paul Ryan, reports that Americans spend an estimated 6 billion hours and more than $160 billion on tax compliance. That dollar figure is not the tax payments, it’s just the tax-related compliance spending on things like software, accountants, and lawyers. A lot of Americans are thinking there has got to be a better way.

The chairman of the Ways and Means Committee, Dave Camp, attracted some attention earlier this year with his tax reform plan, which would lower individual and corporate tax rates while also slapping a new tax on elite college endowments. But Mr. Camp has announced he is retiring Congress, and his plan doesn’t seem to be headed for passage anytime soon.

Lower-profile, but potentially more significant long-term, are the plans offered by two other Republican lawmakers. Mr. Ryan’s budget blueprint mentions them alongside the Camp proposal as “good ideas” and “growth-oriented tax plans.”

One is House Resolution 25, the Fair Tax Act, offered by Congressman Rob Woodall of Georgia. It would repeal all federal corporate and individual income taxes, including payroll taxes, capital gains taxes, and the death tax. It would replace them, and fund the government’s operations, with a new federal consumption tax on goods and services at a 23% rate.

The other is House Resolution 1040, the Flat Tax Act, introduced by Congressman Michael Burgess of Texas. It would give Americans the option of choosing to file with an optional one-page tax return, at a rate of 19% for the first two years and 17% bfor the years after that.

Both the Fair Tax and the Flat Tax are dramatic enough departures from our existing tax code that some skepticism about their prospects is in order. But the encouragement from Mr. Ryan means something; he may take over the tax-writing Ways and Means Committee in the next Congress. Each proposal has backing from other heavyweights among House Republicans.

The Fair Tax has 74 cosponsors, including the chairman of the House Financial Services Committee, Jeb Hensarling, who is a former chairman of the House Republican Conference. The Flat Tax has 11 co-sponsors, including Tom Cole, one of the brightest House Republicans, who is well-respected by many of his peers.

Neither plan is without risk.

Critics of the Fair Tax worry that it will be transformed into something like a European-style value-added tax that exists not as a substitute for the existing income tax system, but as an ever-increasing addition to it. So the Fair Tax’s most far-sighted supporters insist that it be coupled with a repeal of the Sixteenth Amendment.

As for the Flat Tax, though it is designed for simplicity, as long as it is only an option for taxpayers to choose rather than a full replacement for the existing code, it could add complexity for taxpayers rather than removing it. You’d have to calculate your hypothetical taxes twice — under the Flat Tax and under the existing system. Then you’d have to figure out which tax you’d be better off paying, and then make an estimate about future years to determine whether to make the irrevocable decision to switch out of the existing system and into to the Flat Tax.

If these plans advance, expect Democrats to attack them as either giveaways to the rich (the Flat Tax) or attacks on the middle class (the Fair Tax). That’s one reason some Republicans prefer to focus on rate reduction rather than a more dramatic overhaul. Rate reduction functions as a kind of tax reform in its own right by reducing the value of deductions.

As great as the burden of tax-season is for individuals and businesses, it’s one of the many areas where technology has moved faster than the politicians. Electronic filing means that fewer of us have to wait in line at the post office. Tax-preparation software sold by private companies (whose business could be at risk if a major tax simplification ever passed) makes completing those returns easier.

For those of us feeling the frustration nonetheless, the Fair Tax and Flat Tax offer the hope that it may get better, or at least simpler, sometime in the future. It wasn’t so long ago that Herman Cain was dominating the Republican primary discussion with his 9-9-9 plan. If there’s a week of the year for the tax reform policy debate to get some political traction, this is it.

Mr. Stoll is editor of FutureOfCapitalism.com.