"keep within bounds" is correct and is used in spoken and written English.
It means to stay within an agreed upon limit or restriction. Example: I tried to keep within bounds during my budget meeting to avoid any potential conflict.
The budget deficit and money supply were kept within bounds and back taxes began to be collected.
But, so far, the demonstrations have been kept within bounds, and are not doing the Israelis much damage.
Thanks so so much... Best wishes, Kate Fleetwood A Leylandii can be a complete menace if not pruned and kept within bounds on an annual basis.
David Lodge has imagined some details and manufactured some correspondence, detailed in an acknowledgements section, but the novelistic element is kept within bounds.
As part of the deal, the investors have structured the board so that Mr. Citron does not have control over it -- in part, Mr. Weller said, to make sure that Mr. Citron is kept within bounds.
This caused an outcry from businessmen, whose profits Scaevola had kept within bounds; he was prosecuted for "extortion" in 92 and convicted after a trial in which Roman publicani and businessmen unscrupulously used their power among the class that provided criminal juries.
In Billy Elliot, dance is at once an expression of yearning, and a symptom of frustration; Mrs Wilkinson is described as "unfulfilled - that's why she does dancing!" Julie Walters could so easily have given an over-egged and gamey performance as the gutsy mentor, and it is a measure of her intelligence as a performer and Daldry's assurance as a director, that her approach is kept within bounds.
Mr. Meyer has an extraordinary sense of color, and there is also a wit to his designs that he manages to keep within the bounds of good sense.
And to the journalist it says: know your place; cover what we tell you to cover, print our news releases, and keep within your bounds.
In this study we will keep within the bounds of coping through information only.
