We consider greedy contention managers for transactional memory for M × N execution windows of transactions with M threads and N transactions per thread. Assuming that each transaction has duration τ and conflicts with at most C other transactions inside the window, a trivial greedy contention manager can schedule them within τCN time. In this paper, we explore the theoretical performance boundaries of this approach from the worst-case perspective. Particularly, we present and analyze two new randomized greedy contention management algorithms. The first algorithm Offline-Greedy produces a schedule of length O(τ•(C + N log (MN))) with high probability, and gives competitive ratio O(log (MN)) for C ≤ N log (MN). The offline algorithm depends on knowing the conflict graph which evolves while the execution of the transactions progresses. The second algorithm Online-Greedy produces a schedule of length O(τ•(C log (MN) + N log2(MN))), with high probability, which is only a O(log (NM)) factor worse, but does not require knowledge of the conflict graph. Both of the algorithms exhibit competitive ratio very close to O(s), where s is the number of shared resources. Our algorithms provide new tradeoffs for greedy transaction scheduling that parameterize window sizes and transaction conflicts within the window.