The phrase "some little time" is grammatically correct and can be used in written English.
Example: It took some little time for the new employee to adjust to the company's policies and procedures.
The gunfire rattled around these hills for some little time.
For some little time we were cautious, and did not even answer.
It gave me something to fall back into; it gave me some little time to relax".
One could see it creeping along the floor some little time after the woman was gone.
When, after some little time, he got around to announcing his decision, he made it clear that although the case was dismissed, it was not necessarily resolved.
It is probably that after the signature of peace the delegates to the Peace Conference will remain in London some little time to settle such questions as the interchange of prisoners of war.
Some have little time for either, Erin Evers from Human Rights Watch notes.
For some, a little time management and scheduling goes a long way.
As the midnight deadline approached Wednesday, with dinners and cocktail parties wrapping up, some lawmakers wasted little time with their efforts for the third quarter.
Many media commentators, some London-based, some local, who spend little time on the ground in places like the Lower Newtownards Road or Short Strand, bought into the line that this latest conflagration was the result of spontaneous working class loyalist anger.
There were also negative criticism given by some patients, regarding too little time for questions and that some participants took too much time for individual issues.
