We discuss (a bit unusual) behavior of certain NP-complete problems admitting subexponential algorithms. For example, the $ p $-Clustering problem is to decide for a given $ n $-vertex graph $ G $ and integers $ k $ and $ p $, if $ G $ can be turned into a $ p $-cluster (disjoint union of $ p $ cliques) by at most $ k $ edge modifications (adding/deleteling edges). We give a subexponential algorithm solving this problem in time $ O(exp((\sqrt{qp}) +n +m) $. On the other hand, there are strong arguments showing that most of NP-complete problems cannot be solved in subexponential time. While existence of subexponential time algorithms does not resolve P vs NP question, it shows an interesting diversity of the world of intractable problems.