Also, to get back on LTE once already having been in an LTE zone, that tester said it was necessary to unplug the modem and plug it back in again. However, Nelson said that was not necessary, although he did say it could take up to two minutes to reconnect to LTE.

The "hand-off" problem from EVDO to LTE had been foretold by Verizon CTO Tony Melone on Dec. 1. He said there would be a brief delay.

Verizon sells two models of modems for LTE connections to laptops, one from LG and one from Pantech, each for $100 after rebate and a two-year contract.

Nelson said Verizon was working with a modem maker on the hand-off problem, but didn't say which maker. Business Insider said the hand-off problem occurred with an LG model. "We're working with the modem maker for quick update, but no ETA yet," Nelson said.

The spokesman wouldn't say how many modems or data service plans have been sold so far, but said Verizon has been pleased with reviews of network speeds.