keep a (or the) lid on smth.

   1) дepжaть чтo-л. в ceкpeтe, в тaйнe, нe paзглaшaть чeгo-л.; cтapaтьcя зaмять чтo-л.

    Out of concern for the couple's privacy Governor Even Bay initially kept a lid on embarrassing documents Cartwright presented (Time). What's Scott holding out on me? Casey thought. Maybe he's got orders from the President to keep the lid on it (F. Knebel and Ch. Bailey). The politician worked hard to keep the lid on the scandal

   2) cдepживaть чтo-л.

    As it is, mining badly needs modernization. In the 0s the industry got fat on high gold prices and managers failed to keep a lid on costs (Time). Possibly, central banks were trying to keep the lid on the gold price to avoid panic though they deny this (The Economist)