What is known about exact complexity of the shortest superstring problem? Can it be solved faster than $O^\*(2^n)$? Are there known algorithms that solve shortest superstring without reducing to TSP?

UPD: 
$O^\*(\cdot)$ suppresses polynomial factors.

The shortest superstring problem is a problem whose answer is the shortest string which contains each string from a given set of strings. 
The question is about optimization extension of a famous NP-hard problem Shortest Superstring(Garey and Johnson, p.228).