It is not hard to understand why congressional Democrats have chosen to rush ahead with impeachment without waiting for courts to force the testimony of key witnesses.The 2020 election campaign looms, constituents want to hear about something other than Ukraine, and a prolonged process would only strengthen the case that voters, rather than the Senate, should decide whether Donald Trump should be removed from office.Still, it’s painful to consider that senior officials may succeed in dodging congressional subpoenas and accountability — looking at you, Mike Pompeo — and that broad side avenues of the scandal could go unexplored, at least by Congress.Let’s start with the distinct possibility that Trump’s demand that Ukrainian President Volodymyr Zelensky launch politicised investigations in exchange for military aid and a White House meeting was only the last of a series of quid pro quos he forced on Ukrainians.My Washington Post colleague David Ignatius and The New York Times have reported on the suspicious interactions among Trump, his lawyer, Rudy Giuliani, and Zelensky’s predecessor as president, Petro Poroshenko.Giuliani met Poroshenko on at least two occasions in 2017. One meeting, in June, came not long before a meeting that month between Trump and Poroshenko at — yes — the White House.Between the two meetings, Ukraine’s chief prosecutor, Yuri Lutsenko — the same corrupt prosecutor who later promoted false charges against Joe Biden and the US ambassador — had Ukraine’s investigation of secret payments to Trump’s former campaign manager, Paul Manafort, transferred from a special anti-corruption bureau to his office, where it promptly stalled.The second Giuliani-Poroshenko meeting, in late 2017, came not long after Manafort was indicted in the United States, and as the Ukrainians were trying to win approval to buy US Javelin antitank missiles.According to testimony in the impeachment inquiry before Congress, that sale was held up for a while by the Office of Management and Budget — the same agency that halted military aid last summer.According to the Times, the Javelins were finally released in April 2018 — the same month Lutsenko officially ordered the freezing of the Manafort-related cases.Let’s see: a White House meeting and weapons ... for favourable actions on an investigation?There’s no proof. But no wonder Trump complained to Zelensky in their July 25 phone call that “I heard you had a prosecutor who was very good and he was shut down and that’s really unfair”.One of Zelensky’s first acts had been to fire Lutsenko. The prosecutor has also been blamed for Trump’s recall of ambassador Marie Yovanovitch. But the full story behind her dismissal is still not known.Impeachment inquiry chief Adam Schiff has been saying she was removed to clear the way for Trump’s attempt to extort Zelensky.Yet according to the Post, Trump began demanding Yovanovitch’s removal a year earlier, after meeting with two shady Soviet émigré businessmen, Lev Parnas and Igor Fruman.Why did Parnas and Fruman want the ambassador out? It’s still not clear. Yovanovitch testified that she had never met them and knew nothing about their sketchy attempts to strike a deal to export US liquefied natural gas to Ukraine.The two Ukrainians arranged meetings for Giuliani with Lutsenko and other former prosecutors who supplied false stories about Yovanovitch, Joe Biden and the 2016 election. But that came after Trump first targeted Yovanovitch.One person who probably could shed light on this is Rick Perry, the energy secretary, who announced his resignation last month and seems intent on slipping out of town without complying with his congressional subpoena.According to testimony by US Embassy staffer David Holmes, Perry used a meeting with Zelensky to give him a list of “people he trusts” on energy matters.The Times reported that these included a couple of Texas businessmen whom Perry wanted appointed to the supervisory board of the Ukrainian state gas company. That’s the same company Parnas and Fruman were trying to deal with.Holmes said that embassy personnel were subsequently excluded from meetings Perry had with “key Ukrainian energy sector contacts”.Other impeachment testimony identified Perry as a prime intermediary with Giuliani in the brokering of the quid pro quo with Zelensky. Of course, he’s eager to get back to Texas.We may eventually learn more about Ukraine from federal prosecutors in New York, who have already indicted Parnas and Fruman and are said to be looking at Giuliani. But you have to wonder whether Democrats are making a mistake by not pursuing these matters themselves.Yes, it would slow down impeachment. But since there’s almost no chance the Senate will remove Trump, what matters most is that Americans are fully informed about Trump’s corruption before they vote next November.That might be worth a few court cases to enforce subpoenas — or, at least, some more investigation.• Jackson Diehl is deputy editorial page editor of The Washington Post. He is an editorial writer specialising in foreign affairs and writes a biweekly column that appears in print on Mondays