While many smartphones have features that auto-complete words, correct typos on the fly and add punctuation, Mr. Kushler is aiming for the next level.

“We’ve squeezed the desktop computer, complete with keyboard and mouse, into something that fits in a pocket. The information bandwidth has become very constricted,” he said. “I thought, if we can find a better way to input that information, it could be something that would really take off.”

Mr. Kushler says Swype is a big breakthrough that could reach billions of people. That’s not as ambitious as it sounds. To date, the T9 technology has been built into more than four billion devices worldwide. In 1999 its creators sold it to AOL for a reported $350 million; it is now owned by the speech-recognition company Nuance.

Swype’s software detects where a finger pauses and changes direction as it traces out the pattern of a word. The movements do not have to be precise because the software calculates which words a user is most likely trying to spell.

Capitalization and double letters can be indicated with a pause or squiggle, while spacing and punctuation are automatic. Mr. Kushler, who is chief technology officer of Swype, estimates that the software can improve even the nimblest text-messager’s pace by 20 to 30 percent.