Surgery is becoming more available for transgender people as a growing number of academic centers and hospitals offer the procedure and insurance companies provide coverage.

Stacey Parsons, a 45-year-old from Kent, Ohio, had genital surgery in August at Cleveland Clinic, which last year launched a transgender-surgery-and-medicine program. For years the procedure was unattainable for Ms. Parsons because it costs upward of $20,000 and was rarely covered by insurance.

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