Andrew Wright is a law professor who previously served as associate counsel to President Barack Obama in the White House and as staff director of a congressional oversight subcommittee. Follow him on Twitter (@AndyMcCanse). Former Ambassador Norman L. Eisen, a CNN contributor, is a senior fellow at The Brookings Institution and served as President Obama's "ethics czar" from 2009-11. The opinions expressed in this commentary are theirs.

(CNN) As former White House lawyers, we have sought to preserve confidential presidential communications and policy deliberations from disclosure. And we believe that executive privilege has a legitimate, albeit limited, role as a shield.

Executive privilege, including the presidential communications privilege, is an assertion of presidential authority to withhold information from a judicial or congressional proceeding in order to preserve executive branch confidentiality interests.

In prior high-profile criminal investigations with White House equities -- like Iran-Contra, Whitewater/Clinton-Lewinsky, the 1996 campaign financing task force and Valerie Plame's blown CIA cover -- presidents and vice presidents have invariably negotiated about interviews and testimony under the shadow of a subpoena threat.

Usually, out of respect for the White House and in return for a voluntary appearance, prosecutors afford the president certain logistical accommodations, including the right to have counsel present (unlike normal grand jury witnesses).

But President Donald Trump has been flirting with a full-blown subpoena fight. So, the privilege arguments here are part of an effort to undermine Mueller's subpoena threat by suggesting he'll lose.

In its letter to Mueller, President Trump's legal team goes to great lengths to explain the nature and purpose of executive privilege as it relates to presidential communications. The memorandum contains the broad assertion with respect to the White House production of information that "[t]he majority of that information could have been rightfully withheld on multiple privilege grounds, including but not limited to the presidential communications privilege."

In that sense, the memorandum merely establishes that the White House has so far engaged in the typical negotiated cooperation with respect to documents and testimony by the President's aides.

But it is targeted at the coming court fight: President Trump (and special counsel Mueller) will want to have built a record of reasonable accommodation before a judge rules on a subpoena. Mueller's team will have its own perspective on the level of cooperation it has received as the President and his allies continue to publicly attack the special counsel.

More substantively, the memorandum seeks to leverage the Clinton-era case, In re Sealed Case (Espy), to argue that Mueller has not met a standard of need for President Trump's testimony that would support a valid subpoena.

In Espy, the DC Circuit held that the prosecutor must "demonstrate with specificity why it is likely that the subpoenaed materials contain important evidence and why this evidence, or equivalent evidence, is not practically available from another source." Team Trump then makes the case that Mueller's need is lacking.

There are several glaring problems with the Trump executive privilege argument.

First, as a factual matter, the President is a central witness to numerous episodes under investigation. The President's son, son-in-law, campaign chairman, deputy campaign chairman, personal lawyer and four campaign foreign policy advisers (one of whom briefly served as national security adviser and another who became attorney general) have all had Russia connections that have come under scrutiny.

The President's public remarks at various points suggest he may have had more visibility into Russia's efforts to assist his campaign. (For instance, in an interview with The New York Times last fall, the President said (and then denied) that he had advance knowledge of the June 2016 Trump Tower meeting between senior campaign officials and Russians.)

Once inaugurated, President Trump has manifested public and private hostility to the Russia inquiry.

Obstruction of justice -- both in the criminal statute and Nixon and Clinton articles of impeachment senses -- turns on the president's state of mind. There are several different formulations of federal obstruction of justice, but as a general matter, the prosecution must establish proof of an obstructive act or attempt to influence a reasonably foreseeable and proximate federal proceeding with corrupt intent.

Impeachment for obstruction of justice is governed by less rigid standards, but proof of corrupt intent would likely be necessary to demonstrate that the president has abused his power. Documents and other witnesses' testimony certainly shed light on Trump's state of mind, but they are no substitute for asking the man himself.

Second, the two primary privilege cases that would guide any court reviewing a Mueller subpoena -- Espy and United States v. Nixon -- do not support the Trump legal position.

In Espy, the White House documents at issue related to a White House counsel investigation undertaken at the president's direction to see whether to take administrative action against the secretary of agriculture over allegations that he took bribes or accepted gratuities from parties with business before the Department of Agriculture -- the same issue being investigated by the independent counsel.

Neither President Bill Clinton, nor his White House aides, nor his senior campaign staff were under investigation. It is surprising to see the Trump legal team place so much reliance on a case in which the DC Circuit told the trial court to consider ordering more, not less, White House disclosures.

Even more damaging to the Trump cause, though, is Nixon. There, the Supreme Court unanimously upheld the Watergate special prosecutor's subpoena for the Nixon tapes. The court recognized that the president is entitled to assert executive privilege, but that it is a qualified privilege. A qualified privilege means that the court will balance interests in confidentiality against the need for information -- it is not a guaranteed winner for the president.

The court took great pains to balance a president's confidentiality interests against the need for "relevant evidence in a criminal proceeding." Mueller's need for evidence seems more like Nixon than Espy, and the courts enforced subpoenas served on the White House in both.

Finally, like Trump, Nixon argued that he did not need to comply with the special prosecutor's subpoena because the president sits atop the executive branch, the special prosecutor was his subordinate and this was an "intra-branch dispute" not capable of judicial resolution.

The Supreme Court unanimously rejected that argument. While that holding exposes the weakness of President Trump's unitary executive argument, it also undermines his executive privilege argument attacking Mueller's subpoena authority. We are not surprised Nixon was conspicuously absent from the Trump team's memorandum.

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The net effect of the facts here and these two cases, Trump will likely lose a court battle over his sweeping position that he cannot be subpoenaed. We believe such a fight is looming. As suggested by Rudy Giuliani's publicity tour, Mueller is still pressing for an interview and evidently willing to subpoena the President if it is not forthcoming.

As he must, the central questions in the investigation cannot otherwise be resolved. When the courts consider the arguments in the Trump lawyer letter, they will likely end up where they belong -- in the dust bin, requiring him to appear and contest the applicability of the privilege to particular questions just like any other litigant.