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