'greater readiness' is correct and usable in written English.
This phrase can be used to describe a situation where someone is well-prepared or more prepared than before. For example, "John showed greater readiness for the upcoming job interview and was able to answer all the questions confidently."
More efficiency, other things equal, is a good thing; greater readiness to approve any given measure may not be.
While Mr. Bush and Mr. Cheney want greater readiness, they also say they want less involvement by American troops in peacekeeping in Europe and elsewhere.
Mr. Arafat has voiced shock and condemnation of the attacks in the United States, but he has not signaled a greater readiness to comply with Israeli security demands.
International mediators say they detect greater readiness for compromise but Libyans question the credentials of those taking part in negotiations and their ability to make any agreement stick.
American generals have cautiously noted an apparently greater readiness on the part of Syria to clamp down on al-Qaeda and the traffic of insurgents across its border.
Many of Georgia's Western friends would be delighted if someone with an easier personality (and greater readiness to listen to advice) were in charge.
CalSTRS's decision represents a greater readiness by banks, insurance companies and other institutional investors to recognize their growing exposure to environmental, social and governmental risks.
There is now a greater readiness to understand rather than to condemn suicide, but a tendency to conceal suicidal acts still persists.
Herzog, who creates his own problems with a greater readiness even than Hitchcock did, decided to make things that much more difficult for his three-man crew by shooting in 3D.
The Conservative campaign was built on two deep foundations: a public perception that the years of economic malaise were Labour's fault – a function of carelessness with taxpayers' money – and greater readiness to see David Cameron as a natural prime minister.
Saudi pilots have flown sorties against Houthi rebels in Yemen, the Emiratis in Afghanistan, and now against Islamist targets in Libya, a sign perhaps of a greater readiness to act without US leadership.
