The probabilistic quantum teleportation scheme [Phys.Lett.A 305 (2002) 12] is improved via twoseemingly different methods (i.e., the usual ancilla method and the so-called Kraus method), respectively.The essenceof the improvements is to fetch a part from the residues so that the success probability is accordingly increased.The twoimproved versions and a similar protocol proposed by Li et al.[Phys.Rev.A 61 (2000) 034301] are compared mutuallyand discussed.It is found that they are equally efficient and can reach the success probability threshold determined bythe inherent entanglement of the quantum channel.