Inclusion Criteria

DISEASE CHARACTERISTICS:

- Histologically confirmed ovarian epithelial, fallopian tube, or primary peritoneal
cavity carcinoma

- Recurrent or persistent disease

- Measurable disease, defined as at least 1 lesion that can be accurately measured in
at least 1 dimension (longest dimension to be recorded) ≥ 20 mm by conventional
techniques or ≥ 10 mm by spiral CT scan

- Must have at least 1 "target lesion" to be used to assess response on this protocol
as defined by RECIST criteria

- Tumors within a previously irradiated field will be designated as "non-target"
lesions unless progression is documented or a biopsy is obtained to confirm
persistence at least 90 days following completion of radiation therapy

- Must have had 1 prior platinum-based chemotherapeutic regimen for management of
primary disease containing carboplatin, cisplatin, or another organoplatinum compound
and the initial treatment may have included high-dose therapy, consolidation, or
extended therapy administered after surgical or non-surgical assessment

- Patients are allowed, but not required to receive, 2 additional cytotoxic
regimens for management of recurrent or persistent disease with no more than 1
non-platinum, non-taxane regimen

- Patients who have received only 1 prior cytotoxic regimen (platinum-based
regimen for management of primary disease), must meet 1 of the following
criteria:

- Platinum-free interval of < 12 months

- Progressed during platinum-based therapy

- Persistent disease after a platinum-based therapy

- Not eligible for a higher priority GOG protocol (i.e., any active GOG Phase III
protocol for the same patient population)

PATIENT CHARACTERISTICS:

- GOG performance status (PS) 0-2 or after receiving 1 prior treatment regimen (GOG PS
0-1 after receiving 2 or more prior regimens)

- Platelet count ≥ 100,000/mm³

- ANC count ≥ 1,500/mm³

- Hemoglobin > 9 g/dL

- Creatinine ≤ 1.5 times upper limit normal (ULN)

- AST and ALT ≤ 2.5 times ULN

- CPK normal

- Bilirubin or direct bilirubin normal

- Alkaline phosphatase normal

- Neuropathy (sensory and motor) ≤ grade 1

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- No active infection requiring antibiotics (except for uncomplicated UTI)

- No other invasive malignancy within the past 5 years, except nonmelanoma skin cancer

- No known active liver disease or hepatitis

- Willing and able to have a central venous catheter

PRIOR CONCURRENT THERAPY:

- See Disease Characteristics

- Recovered from effects of recent surgery, radiotherapy, or chemotherapy

- At least 1 week since prior hormonal therapy directed at the malignant tumor

- Continuation of hormone replacement therapy allowed

- At least 3 weeks since other prior therapy, including biological and immunological
therapy directed at the tumor

- Chimeric or human or humanized monoclonal antibodies must be discontinued for at
least 6 weeks prior to study entry

- No investigational therapy within the past 30 days

- No prior therapy with docetaxel and/or trabectedin

- No radiation to more than 25% of marrow-bearing areas

- No prior cancer treatment that contraindicates protocol therapy