Spin-transfer-torque magnetic random access memory (STT-MRAM) is a promising emerging memory technology because of its various advantageous features such as scalability, non-volatility, density, endurance, and soft-error immunity. However, high write energy and long write latency are the major obstacles for this technology. The long write latency of the STT-MRAM is primarily due to two reasons. First, the bit-cell switching is asymmetric, which means that one write direction is significantly slower than the other. Second, the stochastic switching behavior of the bit-cell mandates a significant margin for a target write error rate (WER). In this paper, we propose static and dynamic circuit-level techniques to reduce the overall write latency. The static technique reduces the impact of write asymmetry by increasing the write current only for the slow writes. The dynamic technique additionally targets the write margin by dynamically increasing the write current in a stepwise manner to mitigate the negative impact of the stochastic switching behavior. Experimental results show that our proposed dynamic method can reduce the overall write latency by 71% while maintaining the same WER. Applying this technique to a 512 kB L2-cache of a microprocessor improves its performance by 11% and saves energy by 10% on average.