The stonewalling from several key witnesses at the center of President Trump Donald John TrumpBiden says voters should choose who nominates Supreme Court justice Trump, Biden will not shake hands at first debate due to COVID-19 Pelosi: Trump Supreme Court pick 'threatens' Affordable Care Act MORE's dealings with Ukraine is not stopping Democrats from plowing ahead with their fast-moving inquiry.

Rather than wait to secure their testimony, Democrats say they can move forward because other witnesses have corroborated a whistleblower complaint that sparked the inquiry in September.

Democrats continued to hold that view this week, even as they received a favorable court ruling from a judge who ordered former White House counsel Don McGahn to testify in the probe.

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Still, these top officials and figures could help fill out the whole story of what happened as Trump sought to pressure the Ukrainian government to investigate the Bidens and unproven 2016 election interference allegations.

Here are the people who have refused to comply with House Democrats and how they could offer pieces of the puzzle for investigators.

Trump lawyer Rudy Giuliani Rudy GiulianiThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting CIA found Putin 'probably directing' campaign against Biden: report Democrats fear Russia interference could spoil bid to retake Senate MORE

Perhaps no one is as central to the push to get Ukraine’s help investigating Trump’s political opponents as his personal attorney Rudy Giuliani. Democrats have subpoenaed Giuliani for documents, but so far he has refused to comply.

Multiple witnesses have testified that they were told by Trump to work with Giuliani on Ukraine, even though many worried he was a bad influence.

Trump claimed in a recent interview with former Fox News host Bill O'Reilly that he did not direct Giuliani’s involvement in Ukraine.

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"No, I didn't direct him, but he's a warrior. Rudy's a warrior. Rudy went. He possibly saw something," Trump said.

But the White House’s summary of the July 25 call between Trump and Ukrainian President Volodymyr Zelensky shows the president urging the Ukrainian leader to get in touch with Giuliani, saying that “Rudy very much knows what’s happening and he is a very capable guy.”

If he complied with congressional investigators, Giuliani could clear up questions about his involvement in Ukraine.

Acting White House chief of staff Mick Mulvaney Mick MulvaneyOn The Money: House panel pulls Powell into partisan battles | New York considers hiking taxes on the rich | Treasury: Trump's payroll tax deferral won't hurt Social Security Blockchain trade group names Mick Mulvaney to board Mick Mulvaney to start hedge fund MORE

Mulvaney is in a key position to know exactly why Trump wanted to withhold the nearly $400 million in security assistance to Ukraine over the summer.

Democrats have already seized on Mulvaney’s public comments on Oct. 17 acknowledging that the White House used the aid as leverage to push Ukraine to investigate a debunked conspiracy theory blaming the country for 2016 election interference. Mulvaney later tried to walk back his comments.

The Trump aide has rebuffed a subpoena for his testimony as well as documents related to the administration’s decision to withhold the aid. Multiple witnesses have testified that they were told by Mulvaney’s office of the freeze on Ukraine security assistance but were largely in the dark as to why.

And according to The Washington Post, an internal White House review unearthed email exchanges between Mulvaney and budget officials seeking a rationale for holding the aid after Trump had already ordered the freeze.

Former national security adviser John Bolton John BoltonJudge appears skeptical of Bolton's defense of publishing book without White House approval Maximum pressure is keeping US troops in Iraq and Syria Woodward book trails Bolton, Mary Trump in first-week sales MORE

Bolton’s attorney suggested weeks ago that his client had a lot to offer impeachment investigators, though he failed to show up for a requested deposition the day before and has since remained quiet about his time in the White House.

Bolton “was personally involved in many of the events, meetings, and conversations about which you have already received testimony, as well as many relevant meetings and conversations that have not yet been discussed in the testimonies thus far,” his lawyer wrote in a letter to the House general counsel on Nov. 8.

Lawmakers heard from witness testimony that Bolton was frustrated by the efforts led by Giuliani to push for Ukraine to open investigations. Fiona Hill, the former top Russia adviser on the National Security Council, testified that Bolton instructed her to report the enterprise — which he allegedly described as a “drug deal” — to White House lawyers.

Democrats have not subpoenaed Bolton but have said that they’d gladly accept his testimony if he decides to appear voluntarily.

Acting Office of Management and Budget (OMB) Director Russell Vought

Vought oversees the agency that signs off on releasing foreign aid and therefore was in a position to know why and how the Ukrainian security assistance was withheld. But he failed to show up for a deposition under subpoena and has declined to cooperate with the impeachment inquiry.

The only OMB official to break ranks and testify to date has been Deputy Associate Director for National Security Mark Sandy, who said that he and other officials at the agency expressed concerns about aid freeze, with two officials even resigning after voicing frustrations. Sandy, a career official, said that an OMB memo in early August to Vought recommended lifting the hold.

House Democrats have received some documents from OMB in response to their requests.

Democrats on the House Budget Committee released a summary this past week saying that the documents “suggest a pattern of abuse” that is “a troubling deviation from long-standing procedures.” While Democrats did not release the documents, they said that the first formal OMB order to withhold the aid came on July 25, the same day Trump brought up the desired investigations in a phone call with Zelensky.

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Energy Secretary Rick Perry Rick PerryEnergy secretary questions consensus that humans cause climate change OVERNIGHT ENERGY: Democrats push resolution to battle climate change, sluggish economy and racial injustice | Senators reach compromise on greenhouse gas amendment stalling energy bill | Trump courts Florida voters with offshore drilling moratorium OVERNIGHT ENERGY: Trump signs major conservation bill into law | Senate votes to confirm Energy's No. 2 official | Trump Jr. expresses opposition to Pebble Mine project MORE

Perry was part of the U.S. delegation that attended Zelensky’s inauguration in May. The Department of Energy chief and others later briefed Trump on their trip and urged him to meet with Zelensky. But according to testimony from former special envoy Kurt Volker Kurt VolkerGOP senators request details on Hunter Biden's travel for probe Yovanovitch retires from State Department: reports Live coverage: Senators enter second day of questions in impeachment trial MORE, Trump was skeptical of engaging with Ukraine and urged the U.S. officials to "talk to Rudy."

Perry, who declined to show up for a requested deposition, acknowledged in an interview with The Wall Street Journal that Trump directed him to discuss Ukraine corruption concerns with Giuliani. Perry said that he reached out to Giuliani for help with setting up a meeting between Trump and Zelensky.

Ambassador to the European Union Gordon Sondland Gordon SondlandGOP chairman vows to protect whistleblowers following Vindman retirement over 'bullying' Top Democrat slams Trump's new EU envoy: Not 'a political donor's part-time job' Trump names new EU envoy, filling post left vacant by impeachment witness Sondland MORE testified that Perry was included on a July email in which Sondland said Zelensky would tell Trump that he “intends to run a fully transparent investigation and will turn over every stone” in reference to the Ukrainian energy company where Hunter Biden served on the board and the investigation into the 2016 elections.

The Department of Energy pushed back on Sondland’s testimony, saying that Perry spoke to Giuliani only once at Trump’s request. “At no point before, during or after that phone call did the words 'Biden' or 'Burisma' ever come up in the presence of Secretary Perry,” spokeswoman Shaylyn Hynes said.

Vice President Pence

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Trump repeatedly involved Pence in his dealings with Ukraine, even though the vice president has denied knowledge of the efforts to push for the investigations. To date, Pence has refused to provide House Democrats with requested documents.

Jennifer Williams, a foreign service officer detailed to Pence’s office, testified that the vice president initially accepted an invitation from Zelensky to attend his inauguration in May. But a few weeks later, Williams was told that Trump had decided that Pence would not attend.

In late August, Trump canceled a trip to Poland, where he had planned to meet with Zelensky, due to a looming hurricane and sent Pence instead.

Williams testified that Zelensky asked Pence in the Sept. 1 meeting about the hold on U.S. assistance the Ukraine. Pence, according to Williams, said that Ukraine had the "unwavering support" of the United States and "promised to relay their conversation to President Trump that night." She said that neither Pence nor Zelensky discussed the investigations pursued by Trump.

Sondland, who was also in Warsaw, testified that he mentioned to Pence before the meeting with Zelensky that he “had concerns that the delay had become tied to the issue of investigations.” Pence’s office denied that the conversation with Sondland ever happened.

Secretary of State Mike Pompeo Michael (Mike) Richard PompeoWatchdog confirms State Dept. canceled award for journalist who criticized Trump Trump's push for win with Sudan amps up pressure on Congress Putin nominated for Nobel Peace Prize MORE

Testimony from other witnesses indicates that Pompeo was kept in the loop about Giuliani’s shadow foreign policy efforts in Ukraine yet did little to stop it. Pompeo has declined to comply with a subpoena for documents.

Volker testified that he described his “concern” to Pompeo that Giuliani was “projecting a damaging or a negative image about Ukraine, and that's reaching the president.” And Sondland, who was knee-deep in the dealings with Ukrainian officials, testified in his private deposition that he understood “that all of my actions involving Ukraine had the blessing of Secretary Pompeo.”

Pompeo also listened in on the July call between Trump and Zelensky, maintaining in October that it was "consistent" with U.S. policy. Still, investigators could seek more details from Pompeo about the content of the call and whether he thought the discussion of investigations was appropriate.

There are also questions about how much Pompeo did to protect Marie Yovanovitch Marie YovanovitchGrand jury adds additional counts against Giuliani associates Lev Parnas and and Igor Fruman Strzok: Trump behaving like an authoritarian Powell backs Biden at convention as Democrats rip Trump on security MORE, who was ousted as ambassador to Ukraine in May. She testified that she was told by other officials that “there were a number of discussions” between Trump and Pompeo, who “did keep me in place for as long as he could.”