Patient description: The patient is a 37-year-old woman who came to the clinic for a routine Pap smear. The test revealed stage 1B of cervical cancer. The patient tested positive for HPV 16. She has three sexual partners and four children. She underwent tubal ligation. She smokes 30 packs/year and drinks alcohol frequently. She is otherwise healthy. She was offered a radical hysterectomy.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  BRCA1 and BRCA2 Mutation Carrier and BRCAness Phenotype Patients with partially platinum sensitive ovarian cancer (platinum-free interval 6-12 months) who have previously received at least two platinum based chemotherapy lines, BRCA mutated or with BRCAness phenotype Definition of BRCAness phenotype: high-grade serous cancers, great initial sensitivity to platinum drugs and retention of platinum-sensitivity through multiple relapses, long history of disease, long survival, long TFIs between relapses (patients with high personal risk factors will be included after doing the analysis for BRCA 1-2 mutation before knowing the results) BRCA 1 and/or BRCA 2 mutation carriers (patients with established mutation will be included, patients with high personal risk factors will be included after doing the analysis before knowing the results) 2. Patients with platinum resistant ovarian cancer, BRCA mutated or with BRCAness phenotype who have previously received at least two previous chemotherapy lines (including platinum rechallenge). Definition of platinum resistant: Tumor progression within 6 months of completion of platinum-based therapy (after platinum re-challenge for platinum sensitive recurrence). 3. Patient's written informed consent before any clinical trial-specific procedure. 4. 18 years-of-age or older. 5. Measurable disease as defined in the Response Evaluation in Solid Tumors (RECIST) Guidelines 6. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0 or 1. 7. Hematologic variables: 1. Hemoglobin ≥9 g/dL 2. Absolute neutrophil count (ANC) ≥1,500/μL, and 3. Platelet count ≥100,000/μL. 8. Serum creatinine ≤ 1.5 mg/dL or creatinine clearance ≥ 30 mL/min 9. Creatinine phosphokinase (CPK) ≤ 2.5 ULN. 10. Hepatic function variables 1. Total bilirubin ≤ ULN. 2. Total alkaline phosphatase ≤ 2.5 ULN 3. AST (serum aspartate transaminase [SGOT]) and ALT (serum alanine transaminase [SGPT]) must be ≤2.5 x ULN. 11. Albumin ≥ 25 g/l. 12. Adequately recovered from the acute toxicity of any prior treatment. -  Prior exposure to trabectedin. 2. Known hypersensitivity to any of the components of the trabectedin i.v. formulation or dexamethasone. 3. Less than 2 prior chemotherapy lines given in patients with partially platinum sensitive, BRCA mutated or BRCAness phenotype, ovarian cancer recurrences (including platinum rechallenge). 4. Patients with platinum refractory, BRCA mutated or with BRCAness phenotype, ovarian cancer. 5. Less than 4 weeks from last dose of therapy with any investigational agent, or chemotherapy. 6. History of another neoplastic disease (except basal cell carcinoma or cervical carcinoma in situ adequately treated) unless in remission for 3 years or longer. 7. Known clinically relevant CNS metastases. 8. Other serious illnesses, such as: • Congestive heart failure or angina pectoris; myocardial infarction within 1 year before enrollment; uncontrolled arterial hypertension or arrhythmias Psychiatric disorder that prevents compliance with protocol Active viral hepatitis; or chronic liver disease Active infection Any other unstable medical conditions