There is a sound logic to mergers in the market for fixed-line telephones. Mobile connectivity is increasingly marginalizing the business and clouding its prospects. A bunch of small, regional fixed-line operators, this logic goes, will have a much harder time squeezing profit out of the business than a few larger players.

But are things really so bleak for CenturyTel, which said on Thursday it would buy Qwest Communications in a $10.6-billion stock deal? The cost-cutting near-merger-of-equals comes with what might look like a skimpy 15 percent premium to Qwest’s market price, and investors are hardly cheering the news by bidding up stocks. But if growth forecasts for landlines are low, then a the premium probably should be as well.

One possible nugget for investors could be in broadband. CenturyTel said the deal improves its ability to reach customers over its network, deploy new high-speed services to business customers, and expand the availability of broadband connections to consumers.

Last month, regulators released a blueprint for upgrading Internet access for all Americans, with Internet speeds up to 25 times the current average. Part of the plan includes the establishment of a Connect America Fund that would receive up to $15.5 billion over the next decade, using money shifted from the Universal Service Fund that currently supports telephone service for the poor and rural areas. On the face of it, that would sound like a negative for a provider of services to rural communities. But it is no stretch to accept that rural communities are likely to be less served by broadband than urban areas.