Sarah Tew/CNET

iPhone 5S supply continues to try to catch up with demand.

As of Monday, Apple's US online store lists an estimated wait time of three to five business days for all variations of the popular 5S. That's an improvement over the one to two weeks listed a little more than a week ago.

Prior to last week, 5S buyers faced a wait of two to three weeks before the phone would ship.

Since its debut on September 20, the iPhone 5S has seen heavy demand. On launch day, ship time jumped to seven to 10 days within 10 minutes -- and then to October in just under half an hour. But the trend has reversed recently as Apple and its suppliers have worked to satisfy the heavy demand.

Piper Jaffray analyst Gene Munster believes the 5S will follow the same pattern as the iPhone 5, meaning supply will finally catch up with demand around early December.