Inclusion Criteria

DISEASE CHARACTERISTICS:

- Histologically confirmed ovarian epithelial or primary peritoneal cancer

- Recurrent or persistent disease

- Measurable disease

- At least 1 unidimensionally measurable lesion at least 20 mm by conventional
techniques OR at least 10 mm by spiral CT scan

- At least 1 target lesion not in a previously irradiated field

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

- Initial treatment may have included high-dose therapy, consolidation, or
extended therapy administered after surgical or non-surgical assessment

- Platinum-resistant or refractory (i.e., had a treatment-free interval after
platinum therapy of less than 6 months OR disease progression during
platinum-based therapy)

- Patients who have not received a prior taxane may have received a second regimen
that included paclitaxel or docetaxel

- Must not be eligible for a higher priority GOG protocol

PATIENT CHARACTERISTICS:

Age

- Not specified

Performance status

- GOG 0-2

Life expectancy

- Not specified

Hematopoietic

- Absolute neutrophil count ≥ 1,500/mm^3

- Platelet count ≥ 100,000/mm^3

Hepatic

- SGOT ≤ 2.5 times upper limit of normal (ULN)

- Alkaline phosphatase ≤ 2.5 times ULN

- Bilirubin ≤ 1.5 times ULN

Renal

- Creatinine ≤ 1.5 times ULN

Other

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- No active infection requiring antibiotics

- No neuropathy (sensory and motor) > grade 1

- No history of peptic ulcer disease

- No allergies to sulfa or non-steroidal anti-inflammatory drugs

- No known hypersensitivity to paclitaxel or celecoxib

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

PRIOR CONCURRENT THERAPY:

Biologic therapy

- At least 3 weeks since prior biologic or immunologic therapy

- One prior non-cytotoxic* regimen for recurrent or persistent disease allowed NOTE:
*Non-cytotoxic (biologic or cytostatic) agents include (but are not limited to)
monoclonal antibodies, cytokines, and small-molecule inhibitors of signal
transduction

Chemotherapy

- See Disease Characteristics

- Recovered from prior chemotherapy

- No other prior cytotoxic chemotherapy for recurrent or persistent disease, including
retreatment with initial chemotherapy regimen

Endocrine therapy

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

- Concurrent hormone replacement therapy allowed

Radiotherapy

- See Disease Characteristics

- Recovered from prior radiotherapy

- No prior radiotherapy to more than 25% of marrow-bearing areas

Surgery

- See Disease Characteristics

- Recovered from prior surgery

Other

- At least 3 weeks since prior therapy for malignant tumor

- No prior celecoxib

- No prior therapy for a previous cancer that would preclude protocol therapy

- No concurrent amifostine or other protective agents