  In {\sc MaxSat}, we ask for an assignment which satisfies the maximum number
of clauses for a boolean formula in CNF. We present an algorithm yielding a run
time upper bound of $O^*(2^{\frac{1}{6.2158}})$ for {\sc Max-2-Sat} (each
clause contains at most 2 literals), where $K$ is the number of clauses. The
run time has been achieved by using heuristic priorities on the choice of the
variable on which we branch. The implementation of these heuristic priorities
is rather simple, though they have a significant effect on the run time. The
analysis is done using a tailored non-standard measure.
