to run a ship or an organization in an orderly and disciplined manner,firmly and effectively. Or generally to have a good control over something.
Obama says that he intends to run a tight ship
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to exercise a close, strict control over a ship's crew, a company, organization, or the like.
As head master, Dr. Muller is running a tight ship, not allowing even the slightest deviations from his strict rules and regulations.
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She does not have time for fuck boys, disrespect, or foul play of any sort. She expects flowers to her door, and proper accomditations . Her priority is to always be treated as an equal captain on any ship, sea or dry land (anywhere!) any decent lady should Always run a tight ship.
Becky got thrown under the bus for being the worst side piece of the decade BeyoncΓ© explained in her song "I ain't sorry " , that she runs a tight ship and that she's not going for it!