screenshot by Stephen Shankland/CNET

After shipping dates gradually increased over the last two weeks, the black 16GB model of Google's new Nexus 5 smartphone is sold out.

"We are out of inventory. Please check back soon," the Google Play store said of the 16GB black model on Monday.

Shipment times have increased for other models, too. The white 16GB model, which like its black companion costs $350 unlocked, now ships in four to five weeks. The black 32GB model ships in three to four weeks, and the white 32GB model ships in two to three weeks; those cost $400.

The phone comes with Google's version of Android 4.4, aka KitKat, with none of the extra software and user-interface changes that other Android device manufacturers such as Samsung and HTC typically add in. The phone comes with a 5-inch 1920x1080 screen, a 2.26GHz quad-core Qualcomm Snapdragon 800 processor, 2GB of RAM, an 8-megapixel image-stabilized camera, 4G networking using LTE, a 2,300 mAh battery, and wireless charging.

Google and the Nexus 5 manufacturer, LG Electronics, evidently are making phones as they go rather than building a huge inventory of phones in advance. Some Nexus 5 phones dipped briefly out of inventory an hour after going on sale. Since then, Nexus 5 shipment times have been extending. The black 16GB model has consistently showed the longest waits for shipment.

Sprint and T-Mobile are offering pre-orders of the phone, which also works on AT&T's network in the United States. The Nexus 5 doesn't work on Verizon's 4G network, though.