Just because they have released a statement together doesn't mean that the Trump administration and House Republicans agree on much about tax reform. And on Monday, a White House official laid out how the administration wants a bill to be drafted, including some goals that are at odds with those expressed by House Speaker Paul Ryan and other leaders.

President Trump is aiming for a business tax rate of 15 percent, White House legislative director Marc Short told reporters at an event at the Newseum in downtown Washington, an aggressive target for which the administration appears willing to compromise on some of House Republicans' priorities.

Although the White House and top congressional Republicans released a broad outline of agreed-on principles for tax legislation last week, major details are still up for discussion, including the rates on businesses and families.

Short said the White House still favors Trump's originally called-for 15 percent rate, and that that low rate also should apply to businesses that file through the individual side of the tax code, commonly referred to as pass-throughs. A special low rate for pass-through businesses such as partnerships and sole proprietorships is a controversial idea that many economists warn would invite gaming by high-paid professionals. The government would lose about $1 trillion in revenue over a decade as people with high salaries became contractors to take advantage of the special rate, in addition to about $1 trillion in lost revenue from the tax cut, according to the Tax Policy Center.

Aiming for such low rates would create a tension with House Republicans' push for a permanent rewrite of the tax code. Permanence, in their thinking, allows companies to plan over a longer timeline with greater certainty, thereby generating more growth.

To achieve permanent tax reform through the legislative procedure known as reconciliation, however, requires that the legislation not add to federal deficits. In that scenario, Congress would have to eliminate more tax breaks to get lower rates, a daunting political task.

"The key is permanence," House Ways and Means Committee Chairman Kevin Brady, R-Texas, said Monday morning on MSNBC's "Morning Joe." "Tax reform needs to be permanent. To do that, it needs to balance in the budget."

Short suggested Monday that the White House might prefer steeper tax cuts, even if they're only temporary. "We are most interested in making sure the economy is growing," Short said. "I know as far as pulling together the necessary coalitions, there are others who require the deficit-neutrality, and they'll make their case for that."

Similarly, the White House values tax rate reductions over another cherished House Republican priority, allowing businesses to immediately write off all new investments. Tax economists call that policy "full expensing." Short said that full expensing was on the table, but "not the hill we want to die on."

Ryan and other House Republicans have called for enacting full expensing because it would encourage new business investment. In the models used by tax economists in Congress and in outside research groups, new business investment is a main driver of long-term economic growth.

"We think full expensing is probably the single most effective change lawmakers could make to the tax code to encourage additional economic growth and increase incomes," said Kyle Pomerleau, an expert at the Tax Foundation, a nonprofit think tank.

Yet the policy would lose revenue, meaning that including it in the tax bill would mean that revenue could not be applied to further lowering the corporate tax rate. For that reason, some in the broad coalition that the White House is counting on to pass tax reform are not on board. For instance, Americans for Prosperity, the free-market, Koch-affiliated group that hosted Short at the Newseum Monday, is encouraging lawmakers to go for cutting tax rates rather than full expensing, on the grounds that allowing companies to write off all new investments in the year they are made benefits new companies that are adding facilities and machines over old ones that already have built up capital.

As Republicans gear up to start writing actual legislative text in August, some major parts of the plan are still mysteries.

For example, the Republicans' plan for halting the exodus of companies from the U.S. is still unknown. Previously, House Republicans favored a border-adjusted corporate tax that they said would have eliminated the incentives for companies to shift income or their headquarters to low-tax countries. That provision, though, was taken out of the jointly agreed-on principles amid strong opposition from retailers. One alternative that has frequently been raised by tax experts would be a minimum tax on foreign earnings, to prevent companies from routing all their profits through tax havens to lower their taxes. That backup isn't in the administration's plans, Short said, without specifying what tack they might take.

On the personal side of the tax code, administration officials are still considering eliminating a large number of deductions, credits and other breaks to lower tax rates. Other than deductions for charitable giving and mortgage interest, Short said, most breaks are in consideration to be eliminated. Even preferences for retirement savings, such as 401(k)s, are still on the negotiating table.

Treasury Secretary Steven Mnuchin said earlier at the same event Monday that the administration wants to eliminate enough deductions that high-income earners, in particular, might not see a net tax break from lower rates.

"Most people in the top rate, they're not going to get a tax cut," Mnuchin said.

"This is not about a tax cut for the rich," he later added.