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Well, you're half right. NIH is under HHS. On the other hand, as far as the CIA & USPS being the only independent agencies under the federal government...

INDEPENDENT AGENCIES

Advisory Council on Historic Preservation (ACHP)
American Battle Monuments Commission
Central Intelligence Agency (CIA)
Commodity Futures Trading Commission (CFTC)
Consumer Product Safety Commission (CPSC)
Corporation for National Service
Environmental Protection Agency (EPA)
Equal Employment Opportunity Commission (EEOC)
Farm Credit Administration (FCA)
Federal Communications Commission (FCC)
Federal Deposit Insurance Corporation (FDIC)
Federal Election Commission (FEC)
Federal Emergency Management Agency (FEMA)
Federal Energy Regulatory Commission (FERC)
Federal Labor Relations Authority (FLRA)
Federal Maritime Commission
Federal Reserve System:
Board of Governors of the Federal Reserve System
Federal Reserve Banks (via Minneapolis)
Federal Retirement Thrift Investment Board (FRTIB)
Federal Trade Commission (FTC)
General Services Administration (GSA)
Federal Consumer Information Center (Pueblo, CO)
Institute of Museum and Library Services (IMLS)
International Broadcasting Bureau (IBB)
International Joint Commission, Canada and the United States.
Merit Systems Protection Board (MSPB)
National Aeronautics and Space Administration (NASA)
National Archives and Records Administration (NARA)
National Capital Planning Commission (NCPC)
National Commission on Libraries and Information Science (NCLIS)
National Council on Disability
National Credit Union Administration (NCUA)
National Endowment for the Arts (NEA)
National Endowment for the Humanities (NEH)
National Indian Gaming Commission (NIGC)
National Mediation Board (NMB)
National Railroad Passenger Corporation (AMTRAK)
National Science Foundation (NSF)
National Transportation Safety Board (NTSB)
Nuclear Regulatory Commission (NRC)
US Nuclear Waste Technical Review Board (NWTRB)
Occupational Safety and Health Administration (OSHA)
Office of Federal Housing Enterprise Oversight (OFHEO)
Office of Personnel Management (OPM)
Office of Special Counsel (OSC)
Overseas Private Investment Corporation (OPIC)
Peace Corps
Pension Benefit Guaranty Corporation
Postal Rate Commission
Railroad Retirement Board (RRB)
Securities and Exchange Commission (SEC)
Selective Service System (SSS)
Small Business Administration (SBA)
Social Security Administration (SSA)
Tennessee Valley Authority (TVA)
Thrift Savings Plan (TSP)
United States Agency for International Development (USAID)
United States Arms Control and Disarmament Agency (ACDA)
United States International Trade Commission (USITC)
Dataweb (Import/export data)
United States Office of Government Ethics (OGE).
United States Postal Service (USPS)
United States Trade and Development Agency
Voice of America (VOA)

http://www.loc.gov/global/executive/fed.html

Don't feel too bad. At least this time you were half right.