After doing some more cogitating, here's what I'd do if elected Grand Poobah with the 15 cabinet departments:
Agriculture - place under Interior Dept as a subdivision.
Commerce - goes to Interior as subdivision.
Defense - have VA and perhaps Homeland Security placed there as a subdivision.
Education - eliminate
Energy - eliminate
HHS - to Interior
Homeland Security - keep or place under Defense
HUD - to Interior
Interior - now has Agriculture, Commerce, HHS, HUD, Labor, Transportation
Justice - keep
Labor - to Interior
State - keep
Transportation - to Interior
Treasury - keep
VA - to Defense
That leaves:
Defense - VA, Homeland Security (unless violates posse comitatus)
Interior - Agriculture, Commerce, HHS, HUD, Labor, Transportation
Justice
State
Treasury
Energy and Education - eliminated
Now have 5 Secretaries and 8 Undersecretaries. Sell off unnecessary real estate and close all duplicate offices across the nation. Tell duplicate employees they will have to move to where they are needed or be RIFed or take early retirement. Eliminate duplicate or more programs which do the same.