In the case of Wiener v. United States (357 U.S. 349 (1958)), it was recognized that
Congress has the power to create independent agencies; government
entities that are free from the Presidential removal power established in Myers
v. United States (272 U.S. 52 (1926)).
Wiener was a commissioner of
an independent agency (War Claims
Commission), and had been fired by President Eisenhower.
Other exampled of independent
agencies include the Federal Trade
Commission and the Federal Communications Commission.
These agencies don't just
enforce laws (which would make them exclusively Executive Branch
agencies). They also have quasi-legislative and/or quasi-judicial
The President has the power to
appoint people to these offices, but not the power to fire them without
the consent of Congress.
Since these agencies are not
completely Executive Branch in nature, they don't fall exclusively under
the President's purview like Myers did in Myers v. United States.
The idea is that these
agencies need to be able to operate free from Presidential threats,
similar to how the President can't fire a judge.
The concept of these independent
agencies appears nowhere in the
See Buckley v. Valeo (424 U.S. 1 (1976)) which ruled that an
exclusively Executive Branch agency (FEC) could not have officers who
reported to the Legislative Branch.