Identify inhibitors to parallelism. One common class of inhibitor is data dependence, as demonstrated by the Fibonacci sequence above.
Investigate other algorithms if possible. This may be the single most important consideration when designing a parallel application.
Take advantage of optimized third party parallel software and highly optimized math libraries available from leading vendors (IBM's ESSL, Intel's MKL, AMD's AMCL, etc.).a different algorithm to reduce or eliminate unnecessary slow areas