Swansea Council has delayed the transfer of its IT department to Capgemini by a month and cut the number of staff who will join the outsourcing company under the deal.
The council's decision to delay the start of the 10-year outsourcing deal came just three weeks before 73 employees expected to transfer to Capgemini.
IT staff at Swansea went on strike last year when they discovered that the council planned to outsource their department after reading an advertisement.
Although Capgemini has been Swansea's preferred bidder for 12 months, the contract has been delayed and the number of staff to be transferred has been cut from 73 to 66. A contract between Capgemini and the transferring IT staff has yet to be agreed.
Jeff Baker, regional officer of the Unison union, whose members took strike action last year said, "Capgemini was supposed to be in a meeting with us last week about the terms and conditions, but that was postponed."
In a joint statement Swansea and Capgemini said both parties were "pleased with the progress made" in contract negotiations.
Mary Jones, Swansea councillor in charge of "top performance and eGovernment", said, "There are a number of areas where the negotiations will continue over the coming weeks. This period is essential to ensure that the council secures the best possible deal for its employees and customers."
Mark Porter, chief executive at Capgemini, said, "The eGovernment programme is a major undertaking and the decision to defer rather than rush contract signature has to be the right one for all concerned. We keenly anticipate concluding negotiations in the coming weeks."