A generally agreed upon requirement for correctness of concurrent executions in Transactional Memory systems is that all transactions including the aborted ones read consistent values. We denote this as all-reads- consistency. Opacity is a correctness criterion that satisfies the above requirement. A relevant property, which we call as non-interference, is that an aborted transaction should not affect the consistency of the transactions that are executed subsequently. This property is desirable in general and critical for closed nested transactions in the sense that the read steps of an aborted sub-transaction (that were executed before aborting) may make committing its top-level transaction impossible. Recently we proposed a new correctness criterion, Abort Shielded Consistency, that satisfies both all-reads-consistency and non-interference. In this paper, we present an efficient on-line scheduler that implements Abort Shielded Consistency. The scheduler is based on the notion of conflicts which have been appropriately defined for optimistic executions. The scheduler maintains a conflict-graph based on the events executed so far. An event is allowed to be executed only if it does not cause a cycle in the graph. The conflict-graph has separate components for each (parent) sub-transaction. Each component can be maintained autonomously at the site executing the sub-transaction and the checking can be done in a distributed manner. © 2012 Springer-Verlag.