WASHINGTON — Grilled under oath for dozens of hours on Capitol Hill, at least three current and former U.S. officials have all made the same startling admission: a coveted White House visit for the new Ukrainian leader had been explicitly conditioned on his agreeing to investigations that could have helped President Donald Trump’s re-election.

And when Gordon Sondland, the U.S. ambassador to the European Union, was asked point blank, under oath, whether that constituted a "quid pro quo," he did not dispute it, people with knowledge of his testimony said.

As impeachment proceedings march forward, a string of conflicting narratives from Trump, U.S. officials and the Ukrainians has centered on a different question: whether Trump ever overtly linked a freeze in military aid with his demand that President Volodymyr Zelenskiy investigate his political opponents — and when the Ukrainians learned of it. Trump and many Republicans argue that if the Ukrainians were in the dark, any allegation of wrongdoing by Trump falls apart.

"You can’t have a quid pro quo with no quo," Republican Rep. John Ratcliffe, R-Texas, said in comments tweeted out by Trump on Wednesday.

But in some 65 hours of testimony — details of which have been previously reported — along with public comments from Trump, his aides and allies, a portrait is emerging of a quid pro quo that evolved over time, with the president progressively upping the ante when his demands were not met.

What started as a bid to leverage Zelenskiy’s hopes for a White House meeting took on added dimensions as the Ukrainian leader mentioned his desire to buy Javelin missiles from the United States and Trump, in a separate move, put $391 million in military aid on hold.

The evolution of Trump’s efforts to commit the Ukrainians to investigations that could help his re-election may explain the discrepancies in the accounts given to House investigators about whether Trump ever said explicitly that the freeze in aid was linked to his and Trump personal lawyer Rudy Giuliani’s demands — and to whom he might have said it.

In the end, he may not have needed to say it out loud.

Both acting U.S. Ambassador to Ukraine Bill Taylor and former White House official Fiona Hill testified that by early July, the Ukrainians had learned from Trump’s emissaries that Zelenskiy wouldn’t get a White House visit unless he agreed to Giuliani’s demand that he publicly commit to investigate supposed Ukrainian interference in the 2016 election and Burisma, the natural gas company tied to former Vice President Joe Biden’s son Hunter.

Zelenskiy never did commit to the investigations, and wasn’t granted his White House visit.

In the midst of all that, Trump appears to have increased the cost of refusing his demands. He directed that U.S. military assistance scheduled to be delivered to the Ukrainians be unexpectedly held back, as even his acting chief of staff, Mick Mulvaney, has acknowledged.

Taylor, in testimony that Democratic lawmakers described as leaving them gasping, discussed hunting for answers from other U.S. officials about why the aid was frozen after learning about it from a budget staffer on a conference call. Taylor said that one White House official — Alex Vindman — had told him that Sondland had told a top Zelenskiy aide the money wouldn’t flow until Zelenskiy committed to investigate Burisma.

Sondland even told Republican Sen. Ron Johnson of Wisconsin the aid was held up until the Ukrainians agreed to the investigation, Johnson told The Wall Street Journal.

In Sondland’s telling, according to the individuals with knowledge of his testimony, that assertion was based on his own speculation that Trump was applying the same conditions to the military assistance that he had to a Zelenskiy meeting — not on anything Trump explicitly said. In fact, when asked about it separately by both Sondland and Johnson, Trump repeatedly denied there was any quid pro quo, according to Sondland’s testimony, text messages given to Congress and a statement from Johnson. Trump has repeated that assertion in public.

To be sure, the testimony from Sondland — a political appointee and a major donor to Trump’s inauguration who calls himself a “lifelong Republican,” was in many ways less damning to the president than the testimony from career diplomats such as Taylor and former U.S. Ambassador to Ukraine Marie Yovanovitch. The White House has tried to undercut the credibility of their testimony by dismissing them as “radical unelected bureaucrats.”

Yet even on its own, Sondland’s testimony described a tit-for-tat arrangement that meets the basic definition of a quid pro quo. In his deposition, he acknowledged that the conditions were so clear that he and the former U.S. envoy for Ukraine talks, Kurt Volker, conveyed them to the Ukrainians, the individuals said.

Still, Sondland maintained — to the incredulity of many Democrats — that he didn’t know until much later that Burisma was tied to Biden’s son. That assertion and Sondland’s claims that he couldn’t recall other key moments of interest to House investigators led to significant frustration among Democrats, lawmakers and others briefed on his testimony said.

Spokespersons for the House committees conducting the impeachment inquiry declined to comment.

As House investigators seek to piece together the president’s actions on Ukraine over the last several months, they are dependent on a parade of witnesses who each have only partial visibility into what transpired behind the scenes.

Hill and Taylor both testified that the normal channels for conducting diplomacy on Ukraine and keeping relevant officials in the loop were circumvented by Giuliani and a troika of officials deputized by Trump to run a “shadow” policy on Ukraine: Sondland, Volker and Energy Secretary Rick Perry.

And as text messages among many of those individuals show, even they were left struggling in real time to figure out what was happening from their perches in disparate parts of the world: Taylor in Kyiv, Sondland in Brussels, Perry and Hill in Washington and Volker shuttling back and forth between the United States and Ukraine.

A third possible leverage point — Javelin anti-tank missiles — was introduced during Trump’s July 25 phone call with Zelenskiy, the call that prompted a whistleblower complaint and ultimately triggered the impeachment proceedings.

Zelenskiy, according to a memo detailing the call later released by the White House, said Ukraine was “almost ready to buy more Javelins from the United States for defense purposes” against Russian aggression.

“I would like you to do us a favor, though,” Trump immediately replied, before asking Zelenskiy to “find out what happened with this whole situation with Ukraine.” He invoked a debunked conspiracy theory about a hacked Democratic National Committee server ending up in Ukraine and also mentioned Biden’s son.

By that time, the $391 million in military aid had already been suspended, although there are no indications the Ukrainians knew that at the time of the Zelenskiy call. Taylor testified that in his meetings with Ukrainian officials in late July and most of August, the Ukrainians appeared unaware of the freeze, although The New York Times reported Wednesday that the Ukrainians were aware by early August.

The Javelin missiles, though, were separate from the military aid that Trump had quietly suspended in mid-July.

The $391 million in aid to Ukraine was divided into two buckets to be doled out by the State Department and the Defense Department. The State Department funds, for example, were to be given to Ukraine to then use to buy military equipment from U.S. defense manufacturers.

The Javelin missiles, on the other hand, were to have been bought by the Ukrainians using their own money, according to a foreign military sale notification from the Trump administration to Congress. That sale — 150 missiles at a cost of $39 million — was approved earlier this month.

It’s unclear whether Trump, when he responded to Zelenskiy’s missile ask by requesting a favor, was aware that Javelins were not part of the aid he’d just suspended.