And the belief persists amongst opponents that if they can remove dashing opener Sanath Jayasuriya, one of the stars of Sri Lanka's 1996 World Cup winning team, early they are into a vulnerable batting line-up.
"We feel if we can get through their top order we can keep it to a (manageable) score," said Fleming.
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New Zealand's bowling attack, taken apart by Australia during Friday's 215-run thrashing in Grenada, is set to be strengthened by the return of all-rounder Jacob Oram from a right heel problem, and fast bowler Shane Bond from illness.
Oram believes pitch conditions will help New Zealand make good on Fleming's assessment of Sri Lanka's batting.
"The Jamaican pitch is going to have a bit more bounce and seam than we've experienced everywhere else in the West Indies