  We consider bicrossed products obtained by twisting compact semi-direct
products by a suitable finite subgroup. Under some restriction, we give a
practical criterion for the discrete dual of such bicrossed products to have
the rapid decay property (property (RD)). Using this theory, we construct some
examples of discrete quantum groups with (RD) but do not grow polynomially.
Further examples that do not satisfy the hypothesis of our main result are also
constructed.
