Conservative Surgery in Treating Patients With Low-Risk Stage IA2 or IB1 Cervical Cancer

Inclusion Criteria: * Histologically confirmed squamous cell carcinoma of the cervix (any grade) or histologically confirmed grade 1 or 2 adenocarcinoma of cervix * International Federation of Gynecology and Obstetrics (FIGO) stage IA2 or IB1 disease * Tumor diameter =\< 2 cm on physical exam and on imaging studies * No lymphovascular space invasion (LVSI) present on biopsy or previous cone * Less than 10 mm of cervical stromal invasion * Cone margins and endocervical curettage (ECC) specimen negative for invasive cancer, cervical intraepithelial neoplasia (CIN) II, CIN III or adenocarcinoma-in-situ; (a negative margin is defined as no invasive cancer within 1.0 mm of both the endocervical and ectocervical margins and no adenocarcinoma in situ \[AIS\] or CIN II or CIN III at the inked or cauterized margin; one repeat cone and ECC permitted) * Patients are eligible for the study when a cone and ECC are performed prior to pre-enrollment in the study, and pathologic eligibility criteria are met; the cone and ECC must be performed within 12 weeks prior to pre-enrollment in the study; if the cone and ECC performed prior to pre-enrollment do not meet the pathologic criteria, patients may be pre-enrolled and are allowed 1 repeat cone \& ECC after pre-enrollment in order to meet pathologic eligibility criteria * Patients must sign an approved informed consent document * If patient is of childbearing potential, she must have a negative blood or urine pregnancy test within 14 days of surgical treatment on study * Imaging with positron emission tomography (PET) scan, computed tomography (CT) scan of the abdomen and pelvis, and/or magnetic resonance imaging (MRI) of the abdomen and pelvis must be performed and negative for metastatic disease within 12 weeks of enrollment Exclusion Criteria: * Clear cell, neuroendocrine, adenosquamous, serous carcinoma or other high-risk histologies * Grade 3 adenocarcinoma * FIGO stage IA1, IB2, II, III or IV disease * Tumors \> 2 cm in diameter on physical exam or imaging studies * Presence of LVSI * Greater than or equal to 10 mm of cervical stromal invasion * Cone margins or ECC specimen positive for invasive cancer, CIN II, CIN III or adenocarcinoma-in-situ (one repeat cone permitted) * Neoadjuvant radiation therapy or chemotherapy for cervical cancer * Patients unwilling or unable to provide informed consent for the study * Evidence of metastatic disease on PET, CT, and/or MRI performed within 12 weeks of enrollment * Patients who have had a simple hysterectomy (cut through hysterectomy)