Washington (CNN) Donald Trump's Cabinet picks are dropping some of his signature policy positions under the scrutiny of Senate confirmation hearings.

Former ExxonMobil chief Rex Tillerson, retired Gen. John Kelly and Sen. Jeff Sessions -- Trump's picks to run the State Department, the Department of Homeland Security and the Justice Department -- all broke with the President-elect on some major issues.

Here's a look at several breaks between Trump and his nominees that emerged at Senate confirmation hearings this week.

Tillerson on trade, Russia

The biggest breaks came Wednesday from Tillerson, who supported a massive trade deal that Trump has denounced. He also warned of the dangers of Russia and said he'd support providing arms to Ukraine.

Those positions all contrasted in tone and substance from Trump's campaign trail stances.

Tillerson told lawmakers on Wednesday that "I do not oppose" the Trans-Pacific Partnership -- the proposed 12-nation pact that Hillary Clinton once called the "gold standard" of trade deals.

Trump, though, has promised to rip up the Asia-Pacific pact.

Tillerson was also grilled on Russia and told senators he found the US intelligence community's recent report laying out accusations of Russian efforts to hack US political groups to disrupt the 2016 election "troubling." He indicated that cyberbreaches and leaking of stolen email to undermine the democratic process indeed "were undertaken."

Tillerson also said he would have supported providing defensive arms to Ukraine after Moscow's seizure of Crimea, and he spoke to the potential usefulness of sanctioning Russians, both policies at odds with previous statements by Trump.

Homeland Security pick opposes waterboarding

In his confirmation hearing Tuesday, Kelly said he would "absolutely" abide by US laws prohibiting the use of waterboarding and other forms of torture. That was a break with Trump's campaign promise to bring back waterboarding and "worse" forms of torture in the fight against terrorism.

JUST WATCHED DHS pick splits with Trump's campaign promises Replay More Videos ... MUST WATCH DHS pick splits with Trump's campaign promises 02:11

"I don't think we should ever come close to crossing a line that is beyond what we as Americans would expect to follow in terms of interrogation techniques," he said, agreeing that the Geneva Conventions should continue to serve as a guide for the US.

Kelly, the former commander of US Southern Command, also downplayed the importance of one of Trump's central campaign promises: building a wall on the US-Mexico border.

"A physical barrier in and of itself will not do the job. It has to be a layered defense," Kelly said, stressing the need to build partnerships with Latin American countries to combat drug and human trafficking.

Sessions rejects Muslim ban, waterboarding

Sessions also split with the President-elect on waterboarding and rejected his calls for a ban on all Muslims entering the United States.

On waterboarding, Sessions emphasized that Congress has outlawed the practice since it was used in the George W. Bush administration.

"Congress has taken an action now that makes it absolutely improper and illegal to use waterboarding or any other form of torture in the United States by our military and by all our other departments and agencies," he said.

He sought to minimize his conflict with Trump on the President-elect's proposed Muslim ban, saying that Trump has backed away from it, instead saying Trump believes "the focus should be on individuals coming from countries that have histories of terrorism."

JUST WATCHED Sessions: Muslims shouldn't be denied entry to US Replay More Videos ... MUST WATCH Sessions: Muslims shouldn't be denied entry to US 01:39

But he also rejected the idea of a Muslim ban -- which Trump himself has never formally withdrawn, though his aides have.

"I have no belief and do not support the idea that Muslims as a religious group should be denied admission to the United States. We have great Muslim citizens who have contributed in so many ways," Sessions said. "Americans are great believers in religious freedom and the right to exercise their religious beliefs."