Instead of committing to getting the requested assignment done as soon as possible, factor in some buffer time and ask for a couple of days or a week. 

We normally get frustrated and can have a frowning expression when we are interrupted while being busy. When saying a 'no' can be impolite, a better way is to say 'yes' and then asking respectfully to fix a time to discuss.
The best leaders know the value of time and are proactive and ...

Rather than having habitual meetings, make them dynamic and result-oriented. 

Managing time gets challenging as our career progresses and we take up more responsibilities. Five ways we can manage our time like a successful leader:

You need to figure out when your brain works best and get heavy work done in those productive hours.