The invisibility of cylindrical cloaks produced by arbitrary radially coordinate transformations is confirmed. The influence of a tiny geometrical perturbation at the inner boundary of the cloak is investigated. It is shown that a tiny perturbation would induce a noticeable field scattering, due to the slow convergence of the zeroth order scattering coefficients. However, by choosing appropriate coordinate transformation functions, the noticeable scattering can be reduced. More interestingly, the slow convergence can be overcome drastically by putting a PEC (PMC) layer at the interior boundary of the cloak shell for TM (TE) mode.