CNN  — 

Massachusetts Sen. Elizabeth Warren enjoyed a bump in her polling numbers following the second round of Democratic presidential primary debates last week, but she’s still trailing former Vice President Joe Biden, according to a new poll from Quinnipiac University out Tuesday.

Biden leads with 32% of support from Democrats and Democratic-leaning independent voters, followed by 21% for Warren, 14% for Vermont Sen. Bernie Sanders, 7% for California Sen. Kamala Harris, 5% for Mayor Pete Buttigieg, 2% for former Rep. Beto O’Rourke and 2% for New Jersey Sen. Cory Booker.

Warren is up 6 percentage points since Quinnipiac’s last poll, taken before last week’s debate in Detroit. Other candidates remain relatively steady, while Harris took a 5 percentage point dip.

Much of Warren’s bump came from those Democratic voters who consider themselves “very liberal.” Four in 10 said they would support her in the most recent poll, up from 29% in July.

Biden continues to pace the field for the candidate who would be the best leader (33%), but Warren has gained since Quinnipiac’s last poll (up from 17% in July to 22%). Warren also gained in supporters who said she has the best policy ideas (up from 26% in July to 32%), while 17% said Biden and 16% said Sanders.

Regardless, half still think Biden has the best chance of winning against Trump in 2020. Democratic voters slightly prefer a candidate who is more electable (50%) over someone who shares their views (46%). The opposite was true last time the question was asked in March (51% said shares views, 45% most electable).

Warren is also considered to be the one who “won” the debate, according to Democrats and Democratic-leaning independent voters who watched, listened or paid close attention to the debates. Fewer, 15%, said Biden did the best job, 8% for Sanders and Harris each, 7% said Booker, 4% Buttigieg, 3% Gabbard and 2% each name O’Rourke, Yang and Williamson.

Meanwhile, no candidate was overwhelmingly picked for doing the worst job among Democratic voters who watched, listened or paid close attention. Almost 1 in 10 said Biden did the worst job, the same for author Marianne Williamson, while 7% said Harris, 6% said former Rep. John Delaney and 6% said New York City Mayor Bill de Blasio.

The Quinnipiac University poll of Democrats and Democratic-leaning independents was conducted by telephone August 1 through 5 among a random sample of 807 registered voters. Results among the Democratic sample have a margin of sampling error of plus or minus 4.1 percentage points.