 Participants will have one or two treatments with a low dose of rtPA, followed by a blood thinner taken by mouth or by injection for 5 to 7 weeks. On the first treatment day, the patient has a venogram, in which a catheter is placed in an arm vein and passed up to and through the blood clot that is blocking the blood flow in the vein. This is done under an x-ray machine so the radiologist can see exactly where the tube is going. Then, rtPA is injected into the clot about every 30 seconds for 15 to 30 minutes. The catheter is kept in place to maintain access to the vein for additional treatment the next day, if needed. The patient then begins treatment with heparin, either as an outpatient or an inpatient. A second venogram is done the next day. If the venogram shows that the vein is open, anti-clotting treatment with heparin or warfarin continues. If the venogram shows that the vein is still blocked, the rtPA treatment is repeated while the blood thinner treatment continues. The patient has a third venogram the following day. If the vein has opened, heparin and warfarin treatment continues. If the vein is still blocked, the patients participation in the study ends. Although the patient is no longer formally in the study, he or she may choose to receive additional treatments with rtPA in higher doses at NIH or to continue using blood thinners under the direction of the primary physician. 