Fontan's circulation is a unique challenge for the anesthesiologist. Venous pressure is the only source of blood flow for the pulmonary circulation. Patients with such circulation are extremely sensitive to progression of cyanosis (decreased pulmonary blood flow) or circulatory failure. Any major venous compression can compromise the pulmonary blood flow worsening cyanosis; simultaneously, an increased afterload can precipitate circulatory failure. We present a rare patient of surgically corrected Ivemark syndrome with Fontan's physiology with dextrocardia who developed a large uterine fibroid compressing inferior vena cava (IVC). As a result of compression, not only the pulmonary circulation was compromised but she also developed stasis-induced venous thrombosis in the lower limbs that lead to pulmonary embolism (PE) (increased afterload). In addition to oral anticoagulation an IVC filter was inserted to prevent ongoing recurrent PE. Further, to prevent both circulatory compromise and deep venous thrombosis an urgent myomectomy/hysterectomy was planned. In the present case, we discuss the issues involved in the anesthetic management of such patients and highlight the lacunae in the present guidelines for managing perioperative anticoagulation these situations.