Inclusion Criteria

Criteria:

- Histologically confirmed ovarian epithelial, primary peritoneal, or fallopian tube
cancer:

Persistent or recurrent disease

- Measurable disease, defined as >= 1 unidimensionally measurable lesion >= 20 mm by
conventional techniques:

- Must have >= 1 target lesion to assess response;

- Tumors within a previously irradiated field are considered nontarget lesions

- Must have received 1 prior platinum-based chemotherapy regimen (for primary disease)
containing carboplatin, cisplatin, or other organoplatinum compound:

Initial treatment may have included any of the following:

- High-dose therapy;

- Consolidation therapy;

- Extended therapy administered after surgical or nonsurgical assessment

- AND Must have received 1 prior platinum-based chemotherapy regimen (for primary
disease) containing carboplatin, cisplatin, or other organoplatinum compound:

One additional cytotoxic regimen for recurrent or persistent disease allowed

- No history or evidence of CNS disease, including primary brain tumor or brain
metastases

- Zubrod performance status 0-2 (0-1 for patients who received 2 prior regimens [taxane
and/or platinum regimens are counted separately])

- Absolute neutrophil count >= 1,500/mm^3

- Platelet count >= 100,000/mm^3

- Hemoglobin >= 9 g/dL

- Bilirubin normal

- AST and ALT < 2.5 times upper limit of normal (ULN)

- Creatinine < 1.5 times ULN OR creatinine clearance > 60 mL/min

- PT/INR < 1.5 OR in-range INR 2-3 (if patient is on a stable dose of therapeutic
warfarin or low molecular weight heparin)

- PTT < 1.2 times control

- Urine protein:creatinine ratio < 1

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception during and for at least 6 months
after completion of study treatment

- No active infection requiring antibiotics

- No sensory and motor neuropathy >= grade 2

- No history of allergic reactions attributed to compounds of similar chemical or
biologic composition to VEGF Trap, Magnevist, or fludeoxyglucose F 18

- No history of allergic reaction to paclitaxel or docetaxel or to products mixed in
Cremophor EL or Tween 80

- No active bleeding or pathologic condition that would carry a high risk of bleeding,
including any of the following:

Known bleeding disorder; Coagulopathy; Peptic ulcer disease; Diverticulitis; Tumor
involving major vessels

- No active and/or untreated pulmonary embolism, deep vein thrombosis, or other
thromboembolic event (i.e., any condition associated with aberrant clotting or
migration of an induced clot)

- No history or evidence of other CNS disease, including any of the following:

Seizures not controlled with standard medical therapy; Cerebrovascular accident; Transient
ischemic attack; Subarachnoid hemorrhage within the past 6 months

- No clinically significant cardiovascular disease, including any of the following:

Uncontrolled hypertension (i.e., systolic blood pressure [BP] > 150 mm Hg or diastolic BP
> 100 mm Hg; systolic BP > 180 mm Hg and diastolic BP < 90 mm Hg OR diastolic BP > 90 mm
Hg on >= 2 measurements within the past 3 months); Myocardial infarction; Coronary or
peripheral artery bypass graft

- No clinically significant cardiovascular disease, including any of the following:

New York Heart association class III or IV congestive heart failure; Serious cardiac
arrhythmia requiring medication; Peripheral vascular disease >= grade 2; Unstable angina
within the past 6 months; Clinically significant peripheral artery disease (e.g.,
claudication) within the past 6 months

- No known hypersensitivity to Chinese hamster ovary cell products or other recombinant
human or humanized antibodies

- Able to undergo an MRI scan:

No claustrophobia; No implanted devices or metallic foreign bodies not compatible with MRI
(e.g., ferromagnetic implants or pacemakers); No known history of allergic reaction to
gadolinium contrast agents

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

- No significant traumatic injury within the past 28 days

- Recovered from prior therapy to NCI CTCAE v3.0 grade =< 1:

Alopecia allowed

- No prior VEGF Trap

- No prior cancer treatment that would preclude study treatment

- Prior paclitaxel allowed

- Prior docetaxel for primary or recurrent disease allowed provided the following
criteria are met:

No disease progression during therapy; No disease relapse within 3 months of completing
therapy; No persistent disease at the completion of primary therapy

- More than 7 days since prior placement of a vascular access device or core biopsy

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

- At least 4 weeks since other prior therapy, including immunologic agents (6 weeks for
nitrosoureas or mitomycin C)

- More than 28 days since prior major surgery, open biopsy, dental extraction, or other
dental surgery/procedure resulting in an open wound

- No concurrent major surgery

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No other concurrent anticancer therapy

- No other concurrent investigational agents

- No concurrent hematopoietic growth factors during course 1 of phase I

- Concurrent hormone replacement therapy allowed

- WBC >= 3,000/mm^3