• Number of patients with objective response [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  

• The number of patients with an unbiased objective response [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  
• Progression-free survival [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  
• Time to progression [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  
• Overall survival [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  
• Duration of response [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  
• Duration of stable disease [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  
• Cancer antigen 125 (CA125) response [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  
• The number of patients with adverse events [ Time Frame: Up to approximately 3 years ] [ Designated as safety issue: No ]
  

Patients will be enrolled in the study after all study-specific entry criteria are met and informed consent is obtained. Patients will be required to attend regular clinic visits to receive study medication and have their status monitored. Patients will also be required to have radiologic tumor assessments performed at multiple times throughout the study. A detailed explanation can be provided by the study physician (Investigator) conducting this study. Trabectedin at a starting dose of 0.58 mg/m2 will be given to patients intravenously (i.v). as a 3-hour infusion every week for 3 weeks (on Days 1, 8, and 15) of a 4 week cycle via a central venous catheter (also referred to as a "central line" which is a tube ie, "catheter" placed into a large vein). All patients will receive dexamethasone 10 mg i.v. 30 minutes prior to each trabectedin infusion. Patients may receive multiple cycles of trabectedin in the absence of disease progression.