Two fast mutual exclusion algorithms using read-modify-write and atomic read/write registers are presented. The first one uses both compare&swap and fetch&store the second uses only fetch&store. Fetch&store are more commonly available than compare&swap. It is impossible to obtain better algorithms if "time" is measured by counting remote memory references. We were able to maintain the same level of performance with or without the support of compare&swap. However, fairness is degraded from 1-bounded bypass to lockout freedom without the support.