Dwr Cymru said water supplies to homes hit by pipe bursts are improving as its engineers again worked through the night.
The main problems with low pressure remain largely in Powys with issues around Merthyr now resolved.
The company is dealing with around 250 burst mains a day, five times the usual level.
Some customers are having problems contacting its call centre due to unprecedented demand.
There is low pressure in Builth Wells town centre, a burst water main in Llanddoged near Conwy is affecting supply to about 100 properties and there is low pressure in Rhayader affecting just over 1,000 customers.
There is low pressure in Ynysybwl affecting just over 1,000 customers with similar issues in Erwood and surrounding areas in Powys.
Some people in western Carmarthenshire - where at one stage 3,000 homes were without water - say there are still experiencing problems.
Councillor Phillip Hughes of St Clears said they were told on Thursday morning they would have running water within a matter of hours but there were still some properties without a supply including a care home with 14 residents.
"I'm a bit concerned really," he said.
"It's been three days. They have given out bottled water but they do not have water to flush the toilets, bathe and clean.
"I appreciate its difficult and they [Dwr Cymru] are doing their very best but there is a problem with misinformation."
Dwr Cymru said issues affecting Merthyr were resolved overnight and another community that now has running water again after being without since Monday is St Mary's Hill near Bridgend.
Resident Phillip Avery told BBC Radio Wales: "We are one of the lucky ones.
"As much as I was somewhat critical about Dwr Cymru yesterday I can't give them anything but praise for their actions.
"It certainly teaches you not to take water for granted - it's like waking up in a five star hotel today."
He said residents had found it difficult contacting the company by phone and suggested Dwr Cymru improves information available on its website with detailed hourly updates.
A spokesman for Dwr Cymru said: "While the situation is gradually improving, we are aware that there are a small number of customers for whom supplies have not yet returned to normal.
"We are committed to resolving these issues as quickly as possible and will continue to work flat out to do so."
But he said where customers had problems with their own plumbing Welsh Water was unable to help and they should contact a registered plumber.
"Being without tap water is a massive inconvenience and we are grateful that our customers have, by and large, been prepared to bear with us while we deal with the all the problems caused by the record freeze and rapid thaw" he added.
"We would like to apologise for any inconvenience caused by the situation and for any delay people may have experienced in reaching our contact centre."