On Thursday, the hospital urged mothers-to-be to ring before arriving as its neonatal cots were full.
It had said only women in advanced stages of labour who could not travel were being admitted.
But on Friday the hospital said the unit was now accepting most mothers-to-be in labour.
Consultants and senior midwives were said to be assessing each case of premature labour to see if they may still need to go elsewhere.
Although the unit remained extremely busy, caesarean sections and inducements were also now going ahead.
Abertawe Bro Morgannwg University Health Board said: "The neonatal unit, which cares for poorly babies, is still extremely busy but the situation has eased enough for most mums-to-be to have their babies in the hospital.
"Earlier this week the neonatal unit was completely full, meaning that only women who were too advanced in their labour to travel were being accepted and all others were being asked to call ahead in advance.
"The situation is constantly evolving but the service is expected to remain under some pressure for a few days at least."
Women due to give birth at Singleton who go into premature labour - less than 36 weeks into their pregnancy - are asked to call the ward on 01792 205666.

Care worker Alec Wallbank, 30, of Pontypridd, Rhondda Cynon Taff, is alleged to have carried out the offence between July and September 2014 in Cardiff.
He appeared at Cardiff Magistrates Court wearing a black shirt and tie.
He was released on bail and the case was sent to Cardiff Crown Court.
A plea and case management hearing is due to be held on 18 August.

The visitors led 24-0 at the break through a brace from Sneyd and tries from Fetuli Talanoa and Albert Kelly.
Kelly bagged his second after the restart and Josh Griffin and Carlos Tuimavave scored before Sneyd crossed for his third of the evening.
Sam Wood and Oliver Roberts got consolation scores for the Giants in the second half.
Huddersfield stand-off Danny Brough, who needs six points to move up to ninth on the all-time domestic points scorers list, missed both his attempts at goal.
The dominant victory moves the Black and Whites up to second in the Super League table before the rest of the weekend's fixtures.
Huddersfield Giants: Mason, Ormsby, S. Wood, Mellor, McIntosh, Brough, Brierley, Rapira, Leeming, Ikahihifo, Roberts, Smith, Hinchcliffe.
Replacements: Wakeman, Clough, Dickinson, M. Wood.
Hull FC: Shaul, Fonua, Tuimavave, Griffin, Talanoa, Kelly, Sneyd, Taylor, Houghton, Bowden, Manu, Minichiello, Thompson.
Replacements: Connor, Green, Matongo, Washbrook.
Referee: Phil Bentham.
Attendance: 5,176.
Swansea's Singleton Hospital says it is accepting "most" expectant women in labour again after pressures on its neonatal services eased.
[NEXT_CONCEPT]
A deputy manager of a mental health ward has appeared in court accused of engaging in sexual activity with a woman patient.
[NEXT_CONCEPT]
Marc Sneyd scored a hat-trick and kicked eight goals as Hull FC comfortably won at Huddersfield Giants.