This trial will test the efficacy of brief periods of controlled limb ischemia (remote ischemic preconditioning, RIPC) as an effective treatment of patients with Raynaud's Phenomenon (RP).The hypothesis of this trial is that due to its vasoprotective effects, RIPC would be more effective than placebo in the treatment of both primary and secondary RP, as defined by decreased frequency, duration, and severity of attacks. This trial was also designed to monitor the tolerance of RIPC in a rheumatologic population. Patients will not be required to stop any current treatment for RP.