We consider greedy contention managers for transactional memory for M x N execution windows of transactions with M threads and N transactions per thread. Assuming that each transaction conflicts with at most C other transactions inside the window, a trivial greedy contention manager can schedule them within CN time. In this paper, we show that there are much better schedules. We present and analyze two new randomized greedy contention management algorithms. The first algorithm Offline-Greedy produces a schedule of length O(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. The second algorithm Online-Greedy produces a schedule of length O(C log(MN) + N log^2(MN)) with high probability which is only a O(log(NM)) factor worse, but does not require knowledge of the conflict graph. We also give an adaptive version which achieves similar worst-case performance and C is determined on the fly under execution. Our algorithms provide new tradeoffs for greedy transaction scheduling that parameterize window sizes and transaction conflicts within the window.