Let X
i
,i ∈ ℕ, be independent and identically distributed random variables with values in ℕ0. We transform (‘prune’) the sequence {X
1,…,X
n
},n∈ ℕ, of discrete random samples into a sequence {0,1,2,…,Y
n
}, n∈ ℕ, of contiguous random sets by replacing X
n+1 with Y
n
+1 if X
n+1 >Y
n
. We consider the asymptotic behaviour of Y
n
as n→∞. Applications include path growth in digital search trees and the number of tables in Pitman's Chinese restaurant process if the latter is conditioned on its limit value.