Last week's attacks peaked with an effective downing of the Twitter site for just under an hour on Tuesday, although Twitter said in a blog posting that the attack was a minor one, and the company's IT staff are analysing the traffic to prevent a recurrence.
"Twitter continues improving system response such that inevitable denial-of-service attacks such as those we saw last week don't interfere with normal operations", Twitter said in a prepared statement.
"We make every effort to keep folks updated", the statement added.
As reported by Infosecurity, on 6 August a similar attack - apparently directed at crippling the account of a Georgian blogger - caused many social networking and blogging sites to be affected.
The affected sites included YouTube, Facebook and LiveJournal as well.
With around 20 million users, Twitter was the worst affected by the DDOS owing to its relatively small size in social networking terms.
The perpetrators of the DDOS attack have not yet been traced.