“We did see significant interest,” John Stratton, executive vice president at Verizon, said on Monday, speaking at a Deutsche Bank investor conference. “Not surprisingly, the first wave is that you see a lot of our own customers, so that migration has been very substantial.”

After the first wave, Verizon saw “meaningful movement” of people switching from other carriers, he added. “We’re only a couple of weeks into it, so there’s a lot to be learned. We’ll watch and see how the quarter shakes out.”

Verizon hadn’t offered any unlimited plans for about five years before it bowed to the biggest trend in the wireless industry and unleashed its own plan almost one month ago. Starting at $80 for one line and going up to $180 for four lines, Verizon’s plan is more expensive than plans from T-Mobile and Sprint and less than AT&T’s.

Last year, after T-Mobile and Sprint unveiled their new unlimited plans in August, the two smaller carriers experienced an upswing in new subscribers. For the third quarter, Sprint (S) added 347,000 regular monthly, or postpaid, customers and T-Mobile (TMUS) added 857,000. In the same quarter, Verizon lost a net 36,000 and AT&T shed 268,000. Verizon likely will do better in the first quarter of 2017, thanks to its unlimited plan.

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Verizon’s new unlimited plan price was intended to be at the “upper end” in terms of price, Stratton explained, as Verizon still thinks its network is better quality and is therefore worth more to customers. Verizon extended its lead over its three major competitors in the most recent professional survey of network quality performed by Rootmetrics, though those competitors have done better in comparisons done by other sources like Speedtest, which compiles the results of voluntary tests consumers conduct via a smartphone app.

As other Verizon executives have explained to Fortune, Stratton again said that the reason the company decided to offer an unlimited plan was that customers were becoming increasingly impatient with the uncertainty and annoyances of monthly data allowances.

“Tiered plans did a reasonably good job of covering actual requirements,” he said. But another factor that became increasingly important to consumers “is the whole peace of mind factor, the predictability of the bill.”

Stratton’s comments came as wireless industry market research firm Wave7 also found early signs of customer interest in Verizon’s unlimited plan. “Checks indicate that the reaction to the launch of Verizon Unlimited has been strongly positive,” the firm wrote in a report last month.

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Verizon (VZ) has been heavily advertising the unlimited plan, Jeffrey Moore, principal at Wave7, says. The “full court press” stood in stark contrast to AT&T, which opened its unlimited plan to all customers two weeks ago and reduced the price last week, Moore said. AT&T (T) didn’t start running ads marketing its unlimited service until a few days ago.

“We’ll see how this unfolds in March,” he said. “But as of now, AT&T’s unlimited effort is now more than a rate card technicality but it by no means resembles Verizon’s full court press.”

Earlier on Monday, longtime telecommunications analyst Craig Moffett said Verizon’s surprise decision to offer unlimited data plans may be part of a strategy to overwhelm competitors’ wireless networks with traffic. Verizon has invested by far the most among the four major wireless carriers in adding capacity to its network through new cellular sites, particularly smaller sites that can be deployed close together in crowded urban areas, Moffett noted in a report on Monday.

Verizon’s new unlimited plan didn’t offer the lowest price, but it did offer full high-definition quality for streamed video. Video is the fastest growing activity on mobile networks and accounts for a significant share of all traffic.

Sprint, T-Mobile, and AT&T had all previously downgraded customers’ video streams to DVD-quality by default to save bandwidth. AT&T allowed customers to opt for higher-quality video if they wanted, while the other two carriers charged more for the higher quality. But shortly after Verizon’s announcement, T-Mobile and Sprint agreed to include HD video streaming at no extra charge and AT&T expanded its unlimited offer to all its customers after previously only allowing its pay TV customers to sign up. All three moves will ultimately put more traffic pressure on the carriers’ networks.

“Verizon’s counter appears to be a re-assertion of network advantage,” writes Moffett. “They believe that they can create a capacity war that they can win.”