There is the concept of pruning in the original paper[1] which basically removes all fully-spent transaction trails. That does not yield a reasonable upper bound on the size though[2]. Beyond pruning, it seems you need to trust another network component (external wallet, server).

[1] https://en.bitcoin.it/wiki/Scalability#Storage [2] http://bitcoin.stackexchange.com/questions/4650/upper-limit-...