Telecom says nearly all of its 87,000 customers affected by a cyber attack have changed their email passwords.
The trouble began on 9 February when Yahoo! Xtra customers reported corrupting emails being inadvertently sent to their contacts.
The attack led to the cancellation of 60,000 passwords and warnings to all Telecom customers to reset their passwords.
Telecom said on Tuesday that 80%, or 60,000 people, have managed to do so, and it is likely that most of the remainder are inactive accounts that have not been used in the past three months.
The company said wait times for its helpline are down to five minutes, but expects that to increase on Tuesday evening when people finish work.
The Institute of IT Professionals says the cyber attack could start targetting those from other providers.
Chief executive Paul Matthews said it appears that hackers have had full access to the mailboxes of those customers affected.
Mr Matthews said any information gathered could be used more specifically to target others, including customers of other providers who were on the mailing lists of Yahoo! Xtra customers.