Search trees with relaxed balance were introduced with the aim of facilitating fast updating on shared-memory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating, so extensive locking in connection with updates is avoided. Rebalancing is taken care of by background processes, which do only a constant amount of work at a time before they release locks. Thus, the rebalancing and the associated locks are very localized in time as well as in space. In particular, there is no exclusive locking of whole paths. This means that the amount of parallelism possible is not limited by the height of the tree.Search trees with relaxed balance have been obtained by adapting standard sequential search trees to this new paradigm; clearly using similar techniques in each case, but no general result has been obtained. We show how any search tree with local bottom-up rebalancing can be used in a relaxed variant, preserving the complexity of the rebalancing from the sequential case. Additionally, we single out the one high level locking mechanism that a parallel implementation must provide in order to guarantee consistency.